Classical mechanics Books

Book SynopsisClearly written in a conceptual language, it provides readers with an understanding of the dynamic behavior of the instrument, including structural and component dynamics, and various analytical models, such as discrete, finite element, and boundary element models.Trade ReviewFrom the reviews: „…[This is the only book] that deals with the engineering aspects of guitars. Thus it serves a real need for scientifically-oriented guitar makers and aficionados as well as those interested in a broad overview of the world of guitars… The overall broad view of the book makes good reading for those interested in the myriad details involve in constructing a string instrument and then evaluating it scientifically, as the author’s personal building experience and knowledge of a wide variety of guitar construction techniques are put to good use… a significant, commendable addition to the guitar literature in a very broad-ranging book on a very important string instrument."George Bissinger, East Carolina University, EXPERIMENTAL TECHNIQUES (May-June 2009)“French discusses whether the math models are … sufficient to capture the features of acoustic responses that are highly correlated with good sound quality. In conclusion … this book will help luthiers at all levels think more clearly about how to successfully manufacture guitars of high sound quality. The book … particularly valuable to students of guitar construction and repair. For the rest of us, this book makes interesting reading.” (Leo Beranek, International Journal of Acoustics and Vibration, Vol. 14 (2), 2009)“Why do guitars sound like they do, and how do you set about making one? These are central questions addressed … in this attractive new book. … The book is well written, and generously illustrated with interesting … graphs. … a unique and special addition to the literature, and it deserves to be widely read. For anyone contemplating construction of a guitar it will surely be indispensible. Physicists and engineers with musical inclinations, as well as guitar players … are likely to be fascinated.” (Peter V. E. McClintock, Contemporary Physics, Vol. 51 (6), 2010)Table of ContentsHistory of the Guitar.- Acoustics and Musical Theory.- Structure of the Guitar.- Dynamic Behavior.- Analytical Models.- Manufacturing Processes.- Sound Quality.- Guitar Electronics.- Unique Characteristics.

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Book SynopsisFinite Element Analysis Using SOLIDWORKS Simulation 2017 introduces the aspects of Finite Element Analysis (FEA) most important to engineers and designers. Theoretical aspects of FEA are introduced to build a better understanding the operation, while the main focus of the text is on conveying the practical concepts and procedures needed to use SOLIDWORKS Simulation in performing Linear Static Stress Analysis and basic Modal Analysis. This text covers SOLIDWORKS Simulation, with lessons that guide readers from constructing basic truss elements to generating three-dimensional solid elements from solid models. This text takes a hands-on, exercise-intensive approach to all the important FEA techniques and concepts.

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Book SynopsisUnlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity.The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects.The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.Trade ReviewFrom the book reviews:“The aim of the textbook is twofold. First, it is a concise and self-contained quick introduction to the basics of differential geometry, including differential forms, followed by the main ideas of Riemannian geometry. Second, the last two chapters are devoted to some interesting applications to geometric mechanics and relativity. … the book is well written and also very readable. I warmly recommend it to specialists in mathematics, physics and engineering, especially to Ph.D. students.” (Miroslaw Doupovec, zbMATH 1306.53001, 2015)Table of ContentsDifferentiable Manifolds.- Differential Forms.- Riemannian Manifolds.- Curvature.- Geometric Mechanics.- Relativity.

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Book SynopsisDas Niveau dieser Aufgabensammlung, die auch auf Schwingungsprobleme von Einmassenschwingern eingeht, entspricht den Maschinenbaustudiengängen an Fachhochschulen. Das Buch eignet sich ferner zum Einstieg an Universitäten und Technischen Hochschulen. Kinematik des Punktes Kinetik des Massenpunktes Kinetik des Körpers bei Drehung um eine feste Achse Kinetik der allgemeinen ebenen Bewegung.Table of ContentsKinematik des Punktes.- 1 Skalare Kinematik — geradlinige und geführte Bewegung.- 2 Vektorkinematik — allgemeine Bewegung.- Kinetik des Massenpunktes.- 3 Dynamisches Grundgesetz der Translation und Prinzip von D’Alembert.- 4 Arbeit, Energie, Leistung.- 5 Freie, ungedämpfte Schwingungen des Massenpunktes.- Kinetik des Körpers bei Drehung um feste Achse.- 6 Massenträgheitsmomente bezüglich Hauptachsen und dazu paralleler Achsen.- 7 Dynamisches Grundgesetz der Rotation.- 8 Arbeit, Energie, Leistung.- 9 Drehimpuls (Drall).- Kinetik der allgemeinen, ebenen Bewegung.- 10 Dynamisches Grundgesetz der ebenen Bewegung.- 11 Freie, ungedämpfte Schwingungen einer Masse.- 12 Freie und erregte Schwingungen einer Masse mit geschwindigkeitsproportionaler Dämpfung.- 13 Kinetik der Relativbewegung.

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Book SynopsisDieses Lehrbuch der Technischen Mechanik besticht durch seine anschaulichen Abbildungen und die didaktisch ansprechende Herangehensweise.Teil 1 beschreibt umfassend die Grundlagen der Statik starrer Körper. Dazu werden für ebene und räumliche Kraftsysteme die axiomatisch begründeten Lösungen für drei Grundaufgaben (Reduktion, Gleichgewicht und Zerlegung einer Kraft) bereitgestellt. Neu gegenüber vergleichbaren Lehrbüchern ist die umfassende Darstellung zur Kinematik starrer Körper sowie die Lösung von Gleichgewichtsaufgaben mit numerischen Methoden.Teil 2 behandelt praktische Problemstellungen zu Schwerpunkten, Balkentragwerken, Fachwerken, Reibung und Arbeitsprinzipien. Neu gegenüber vergleichbaren Lehrbüchern ist ein umfassendes Kapitel über Werkzeuge und Maschinen.Zahlreiche durchgerechnete Beispiele sowie Übungsaufgaben mit Lösungen aus verschiedenen Ingenieurbereichen ergänzen jedes Kapitel. Das Lehrbuch erscheint jetzt in der 2. Auflage. Alle Kapitel wurden überarbeitet, insbesondere die Kapitel zur Kinematik und zu Schwerpunkten wurden neu strukturiert und ergänzt. Weiterhin wurden die Lösungen zu den Übungsaufgaben überarbeitet und weitgehend vervollständigt.Table of ContentsEinleitung.- Teil I Grundlagen der Statik: Grundbegriffe.- Zentrale und nichtzentrale Kraftsysteme in der Ebene und im Raum.- Kinematik von Starrkörpersystemen.- Teil II Anwendungen der Statik: Schwerpunkte.- Balkentragwerke.- Fachwerke.- Werkzeuge und Maschinen.- Schnittgrößen.- Reibung.- Arbeit, Potenzial und Stabilität.

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Book SynopsisDas Repetitorium für Vordiplom, Bachelor- und Zwischenprüfung stellt alle Inhalte zur Experimentalphysik klar gegliedert dar. Zum Buch gibt es ein herausnehmbares Kurzrepetitorium, das alle Kapitel nochmals für die Prüfung zusammenfasst. Zweifarbige Abbildungen, Tabellen, Anwendungsbeispiele und zahlreiche Versuche sind ein besonderes Plus. Die dritte Auflage wurde neu bearbeitet und aktualisiert.Table of ContentsEinführung in Thema und Erscheinungswelt der Physik.- Einführung in Thema und Erscheinungswelt der Physik.- Mechanik.- Kinematik.- Einführung in die Dynamik.- Energie und Energiesatz.- Impuls und Impulserhaltungssatz.- Drehimpuls, Drehmoment, Drehimpulssatz.- Drehbewegungen starrer Körper.- Elastische Kräfte und deren molekulare Grundlagen.- Ruhende Flüssigkeiten und Gase.- Strömende Flüssigkeiten und Gase.- Schwingungen.- Wellen.- Wärme und Statistik.- Grundtatsachen der Wärmelehre.- Grundzüge der kinetischen Gastheorie.- Erster Hauptsatz der Wärmelehre.- Kreisprozesse und zweiter Hauptsatz der Wärmelehre.- Statistische Transportphänomene.- Stoffe in verschiedenen Aggregatzuständen.- Electromagnetismus.- Elektrostatik.- Gleichströme.- Stationäre Magnetfelder.- Magnetische Induktion.- Materie im Magnetfeld.- Stationäre Wechselströme.- Aktive Bauelemente.- Maxwellsche Gleichungen und elektromagnetische Wellen.- Licht und Optik.- Natur und Eigenschaften des Lichts, seine Wechselwirkung mit Materie.- Optische Abbildung.- Interferenz und Beugung von Licht.- Strahlungsgesetze. Kurzrepetitorium Experimentalphysik.

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Book SynopsisWie bewegt sich ein Körper? Was ist das Prinzip der kleinsten Wirkung? Sind Symmetrien grundlegend? Leonard Susskind und George Hrabovsky erklären nicht alles, was es über die Klassische Mechanik zu wissen gibt – sondern alles Wichtige. Begeisterte Physik-Amateure bekommen die notwendige Mathematik und die Formeln an die Hand, die sie für ein wirkliches Verständnis benötigen. Mit glasklaren Erklärungen, witzigen und hilfreichen Dialogen und grundlegenden Übungen erklären die Autoren die Klassische Mechanik so einfach wie möglich, aber nicht einfacher.Table of Contents1 Das Wesen der klassischen Physik.- 2 Bewegung.- 3 Dynamik.- 4 Systeme mit mehr als einem Teilchen.- 5 Energie.- 6 Das Prinzip der kleinsten Wirkung.- 7 Symmetrien und Erhaltungssätze.- 8 Hamilton-Mechanik und Zeit-Invarianz.- 9 Der Fluss im Phasenraum.- 10 Poisson-Klammer und Symmetrien.- 11 Elektrische und magnetische Kräfte.- 12 Zentralkräfte und Planetenbahnen.

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Book SynopsisThis book addresses a range of basic and essential topics, selected from the author's teaching and research activities, offering a comprehensive guide in three parts: Statics, Kinematics and Kinetics. Chapter 1 briefly discusses the history of classical and modern mechanics, while Chapter 2, presents preliminary knowledge, preparing readers for the subsequent chapters. Chapters 3 to 7 introduce statics, force analysis, simplification of force groups, equilibrium of the general coplanar force group, and the center of the parallel force group. The Kinematics section (Chapters 8 to 10), covers the motion of a particle, basic motion and planar motion of a rigid body.Lastly, the Kinetics section (Chapters 11 to 14) explores Newton’s law of motion, theorem of momentum, theorem of angular momentum, and theorem of kinetic energy. With numerous examples from engineering, illustrations, and step-by-step tutorials, the book is suitable for both classroom use and self-study. After completing the course, students will be able to simplify complex engineering structures and perform force and motion analyses on particles and structures, preparing them for further study and research. The book can be used as a textbook for undergraduate courses on fundamental aspects of theoretical mechanics, such as aerospace, mechanical engineering, petroleum engineering, automotive and civil engineering, as well as material science and engineering.Table of ContentsPreface.- Preliminary knowledge.- Fundamentals of statics.- Force analysis.- Simplification of a force group.- Equilibrium of the general coplanar force gruop.- Center of the parallel force group.- Motion of a particle.- Basic motion of the rigid body.- Planar motion of the rigid body.- Newton’s laws of motion.- Theorem of momentum.- Theorem of angular momentum.- Theorem of kinetic energy.- Summary.

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Book SynopsisPart A Solid Mechanics Topics Chap.  1 Analytical Mechanics of Solids.- Chap. 2 Materials Science for the Experimental Mechanist.- Chap. 3 Polymers and Viscoelasticity.- Chap. 4 Composite Materials.- Chap. 5 Fracture Mechanics.- Chap. 6 Active Materials.- Chap. 7 Biological Soft Tissues.- Chap. 8 Ionic Polymer-Metal Composites.- Chap. 9 MEMS and NEMS.- Chap. 10 Hybrid Methods. Chap. 11 Statistical Analysis of Experimental Data.Part B Contact Methods Chap. 12 Electrical Resistance Strain Gages.- Chap. 13 Extensometers.- Chap. 14 Fiber Strain Gages.- Chap. 15 Residual Stress Measurement.- Chap. 16 Nanoindentation.- Chap. 17 Atomic Force Microscopy.Part C Noncontact Methods Chap. 18 Basics of Optics.- Chap. 19 Image Analysis and Processing.- Chap. 20 Digital Image Correlation.- Chap. 21 Geometric Moiré.- Chap. 22 Moiré Interferometry.- Chap. 23 Speckle Methods.- Chap. 24Table of ContentsPart A Solid Mechanics Topics Part A presents topics that fall within the purview of solid mechanics. The first five chapters cover familiar ground, but the next four present new material systems along with the new topics of MEMS and NEMS. The last two chapters describe methods of interpreting the results of tests.Chap. 1 Analytical Mechanics of Solids Chap. 2 Materials Science for the Experimental Mechanist Chap. 3 Polymers and ViscoelasticityChap. 4 Composite MaterialsChap. 5 Fracture MechanicsChap. 6 Active MaterialsChap. 7 Biological Soft Tissues Chap. 8 Ionic Polymer-Metal CompositesChap. 9 MEMS and NEMSChap. 10 Hybrid MethodsChap. 11 Statistical Analysis of Experimental DataPart B Contact Methods Part B starts with three practical chapters on the ‘backbones’ of experimental solid mechanics – strain gages and extensometers – followed by another mainstay – residual stress measurement. Nanoindentation is becoming more widely used for material property determination as is atomic force microscopy.Chap. 12 Electrical Resistance Strain GagesChap. 13 ExtensometersChap. 14 Fiber Strain GagesChap. 15 Residual Stress MeasurementChap. 16 NanoindentationChap. 17 Atomic Force MicroscopyPart C Noncontact Methods Part C is an overview of the rich field of optical methods in the first eight chapters ranging from modern versions of established such as photoelasticity to newer ones based on image analysis. Non-contacting methods at other wavelengths are described in the last three chapters.Chap. 18 Basics of OpticsChap. 19 Image Analysis and ProcessingChap. 20 Digital Image CorrelationChap. 21 Geometric MoiréChap. 22 Moiré InterferometryChap. 23 Speckle MethodsChap. 24 HolographyChap. 25 PhotoelasticityChap. 26 Thermoelastic Stress AnalysisChap. 27 Photoacoustic Characterization of MaterialsChap. 28 X-Ray Stress AnalysisPart D ApplicationsPart D presents applications of the methods and topics of the three previous parts to selected topics – all of which are new and important areas of modern technology. These are examples that demonstrate the breadth and depth of experimental solid mechanics.Chap. 29 Optical MethodsChap. 30 Mechanical Testing at the Micro/Nano ScaleChap. 31 Biological Tissue TestingChap. 32 Biomedical Devices and Biologically Inspired MaterialsChap. 33 High Strain Rate and Impact TestingChap. 34 Delamination MechanicsChap. 35 Structural Testing ApplicationsChap. 36 Electronic PackagingAbout the Authors.- Subject Index

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Book SynopsisThis unique volume introduces the reader to the mathematical language for complex systems and is ideal for students who are starting out in the study of stochastical dynamical systems. Unlike other books in the field, it covers a broad array of stochastic and statistical methods.Table of ContentsFrom the Contents: Stochastic Processes and Complex Systems/ Random Variables/ Analysis of Stationary Data/ Deduction of Models from Data/ Classification Methods/ Basic Equations for Stochastic Processes/ Master Equations/ Numerical Methods for the Solution of Master Equations/ Stochastic Differential Equations: Analytical Procedures/ Numerical Methods for Stochastic Differential Equations/ Functional Integrals in Stochastics/ Perturbation Theory and Approximations that Go Further/ Time Series/ Linear Models for Stochastic Processes

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Book SynopsisStatistical mechanics is one of the most important areas of physics, and it also has applications to subjects as diverse as economics, social behavior, algorithmic theory, and evolutionary biology. This bokk introduces important developments in classical statistical mechanics, and guides readers to the very threshold of research.Trade Review"Unlike typical textbooks ... [Statistical Mechanics in a Nutshell] presents statistical mechanics as a more general theory with broader applications... A graduate student or researcher who wants to explore the applications of statistical mechanics would be very well served by this book."--Choice "Peliti's Statistical Mechanics in a Nutshell is a fantastic reference for those who know the subject, teach it, or need a quick technical reminder, especially on the topic of phase transitions, which are consistently featured in modern-day discussions... Statistical Mechanics in a Nutshell provides the more general overview, with topics such as the renormalization group method. It includes a good mix of fundamental thermodynamics, phase behaviour, and other key subjects."--Physics TodayTable of ContentsPreface to the English Edition xi Preface xiii Chapter 1: Introduction 1 1.1 The Subject Matter of Statistical Mechanics 1 1.2 Statistical Postulates 3 1.3 An Example: The Ideal Gas 3 1.4 Conclusions 7 Recommended Reading 8 Chapter 2: Thermodynamics 9 2.1 Thermodynamic Systems 9 2.2 Extensive Variables 11 2.3 The Central Problem of Thermodynamics 12 2.4 Entropy 13 2.5 Simple Problems 14 2.6 Heat and Work 18 2.7 The Fundamental Equation 23 2.8 Energy Scheme 24 2.9 Intensive Variables and Thermodynamic Potentials 26 2.10 Free Energy and Maxwell Relations 30 2.11 Gibbs Free Energy and Enthalpy 31 2.12 The Measure of Chemical Potential 33 2.13 The Koenig Born Diagram 35 2.14 Other Thermodynamic Potentials 36 2.15 The Euler and Gibbs-Duhem Equations 37 2.16 Magnetic Systems 39 2.17 Equations of State 40 2.18 Stability 41 2.19 Chemical Reactions 44 2.20 Phase Coexistence 45 2.21 The Clausius-Clapeyron Equation 47 2.22 The Coexistence Curve 48 2.23 Coexistence of Several Phases 49 2.24 The Critical Point 50 2.25 Planar Interfaces 51 Recommended Reading 54 Chapter 3: The Fundamental Postulate 55 3.1 Phase Space 55 3.2 Observables 57 3.3 The Fundamental Postulate: Entropy as Phase-Space Volume 58 3.4 Liouville's Theorem 59 3.5 Quantum States 63 3.6 Systems in Contact 66 3.7 Variational Principle 67 3.8 The Ideal Gas 68 3.9 The Probability Distribution 70 3.10 Maxwell Distribution 71 3.11 The Ising Paramagnet 71 3.12 The Canonical Ensemble 74 3.13 Generalized Ensembles 77 3.14 The p-T Ensemble 80 3.15 The Grand Canonical Ensemble 82 3.16 The Gibbs Formula for the Entropy 84 3.17 Variational Derivation of the Ensembles 86 3.18 Fluctuations of Uncorrelated Particles 87 Recommended Reading 88 Chapter 4: Interaction-Free Systems 89 4.1 Harmonic Oscillators 89 4.2 Photons and Phonons 93 4.3 Boson and Fermion Gases 102 4.4 Einstein Condensation 112 4.5 Adsorption 114 4.6 Internal Degrees of Freedom 116 4.7 Chemical Equilibria in Gases 123 Recommended Reading 124 Chapter 5: Phase Transitions 125 5.1 Liquid-Gas Coexistence and Critical Point 125 5.2 Van der Waals Equation 127 5.3. Other Singularities 129 5.4 Binary Mixtures 130 5.5 Lattice Gas 131 5.6 Symmetry 133 5.7 Symmetry Breaking 134 5.8 The Order Parameter 135 5.9 Peierls Argument 137 5.10 The One-Dimensional Ising Model 140 5.11 Duality 142 5.12 Mean-Field Theory 144 5.13 Variational Principle 147 5.14 Correlation Functions 150 5.15 The Landau Theory 153 5.16 Critical Exponents 156 5.17 The Einstein Theory of Fluctuations 157 5.18 Ginzburg Criterion 160 5.19 Universality and Scaling 161 5.20 Partition Function of the Two-Dimensional Ising Model 165 Recommended Reading 170 Chapter 6: Renormalization Group 173 6.1 Block Transformation 173 6.2 Decimation in the One-Dimensional Ising Model 176 6.3 Two-Dimensional Ising Model 179 6.4 Relevant and Irrelevant Operators 183 6.5 Finite Lattice Method 187 6.6 Renormalization in Fourier Space 189 6.7 Quadratic Anisotropy and Crossover 202 6.8 Critical Crossover 203 6.9 Cubic Anisotrophy 208 6.10 Limit n 209 6.11 Lower and Upper Critical Dimensions 213 Recommended Reading 214 Chapter 7: Classical Fluids 215 7.1 Partition Function for a Classical Fluid 215 7.2 Reduced Densities 219 7.3 Virial Expansion 227 7.4 Perturbation Theory 244 7.5 Liquid Solutions 246 Recommended Reading 249 Chapter 8: Numerical Simulation 251 8.1 Introduction 251 8.2 Molecular Dynamics 253 8.3 Random Sequences 259 8.4 Monte Carlo Method 261 8.5 Umbrella Sampling 272 8.6 Discussion 274 Recommended Reading 275 Chapter 9: Dynamics 277 9.1 Brownian Motion 277 9.2 Fractal Properties of Brownian Trajectories 282 9.3 Smoluchowski Equation 285 9.4 Diffusion Processes and the Fokker-Planck Equation 288 9.5 Correlation Functions 289 9.6 Kubo Formula and Sum Rules 292 9.7 Generalized Brownian Motion 293 9.8 Time Reversal 296 9.9 Response Functions 296 9.10 Fluctuation-Dissipation Theorem 299 9.11 Onsager Reciprocity Relations 301 9.12 Affinities and Fluxes 303 9.13 Variational Principle 306 9.14 An Application 308 Recommended Reading 310 Chapter 10: Complex Systems 311 10.1 Linear Polymers in Solution 312 10.2 Percolation 321 10.3 Disordered Systems 338 Recommended Reading 356 Appendices 357 Appendix A Legendre Transformation 359 A.1 Legendre Transform 359 A.2 Properties of the Legendre Transform 360 A.3 Lagrange Multipliers 361 Appendix B Saddle Point Method 364 B.1 Euler Integrals and the Saddle Point Method 364 B.2 The Euler Gamma Function 366 B.3 Properties of N-Dimensional Space 367 B.4 Integral Representation of the Delta Function 368 Appendix C A Probability Refresher 369 C.1 Events and Probability 369 C.2 Random Variables 369 C.3 Averages and Moments 370 C.4 Conditional Probability: Independence 371 C.5 Generating Function 372 C.6 Central Limit Theorem 372 C.7 Correlations 373 Appendix D Markov Chains 375 D.1 Introduction 375 D.2 Definitions 375 D.3 Spectral Properties 376 D.4 Ergodic Properties 377 D.5 Convergence to Equilibrium 378 Appendix E Fundamental Physical Constants 380 Bibliography 383 Index 389

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Book SynopsisWhy do you switch from walking to running at a specific speed? Why do tall trees rarely blow over in high winds? And why does a spore ejected into air at seventy miles per hour travel only a fraction of an inch? Comparative Biomechanics is the first and only textbook that takes a comprehensive look at the mechanical aspects of life--covering animalTrade Review"[T]his is a fantastic book! ... [T]here can be no doubt, this is a science book of the highest and finest quality. Students in biology and physics, including (mechanical) engineers, will find in this book a sound guideline for an alternative view of their respective disciplines. It is a source of inspiration, also for the interested layman, for further reflection on the realm of physics in the biological world."--Harold Heatwole, Integrative and Comparative BiologyTable of ContentsPreface vii PART ONE Life's Physical Context 1 1 Preambulations 3 2 Setting the Stage 11 3 More Tools 29 PART TWO Fluids 51 4 Gases and Liquids: Fluids at Rest 53 5 Gases Meet Liquids: The Interface 71 6 Viscosity and the Patterns of Flow 87 7 The Forces of Flow 111 8 Fluid Events Near Surfaces 141 9 Where Flows Are Inside 163 10 More about Circulatory Systems 183 11 Flows in Small Worlds 207 12 About Lift 225 13 Thrust for Flying and Swimming 251 14 Motion at the Air-Water Interface 271 PART THREE Solids and Structures 285 15 A Matter of Materials 287 16 Biological Materials: Tuning Properties Properly 313 17 Biological Materials: Cracks and Composites 329 18 More about Complex Materials: Viscoelasticity 347 19 Simple Structures: Beams, Columns, Shells 363 20 Less Simple Structural Matters 389 21 Hydrostatic Structures, Hydraulic Devices 407 22 Structural Systems 425 23 Motility and Mobility 449 24 Using Muscle: Tuning and Transmissions 473 25 Getting Around on Land 491 PART FOUR The Contexts of Biomechanics 513 26 Loose Ends and Perspectives 515 APPENDICES 1 Quantification: Rules of the Road 537 2 Motion and Direction 547 3 Size and Scaling 553 List of Symbols 565 References and Index of Citations 567 Subject Index 601

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Book SynopsisPlants and animals interact with each other and their surroundings, and these interactions--with all their complexity and contingency--control where species can survive and reproduce. In this comprehensive and groundbreaking introduction to the emerging field of ecological mechanics, Mark Denny explains how the principles of physics and engineeringTrade Review"Denny's opus features 24 chapters with 778 numbered equations and many illustrative graphs on more than 500 pages. Despite this wealth of information, it makes for an excellent and enjoyable read."--Gregor Kalinkat, Basic and Applied Ecology

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Book SynopsisThis book is an adventure into the computer analysis of three dimensional composite structures using the finite element method (FEM). Once the basic philosophy of the method is understood, the reader may expand its application and modify the computer programs to suit particular needs.Trade Review`The book is highly recommended as a reference text for advanced undergraduate students, as a graduate course on the FE analysis of composites, and as a reference work for both researchers in laboratories and practising engineers in industry.' Zentralblatt MATH, 906 Table of ContentsPreface. 1. Some Results from Continuum Mechanics. 2. A Brief History of FEM. 3. Natural Modes for Finite Elements. 4. Composites. 5. Composite Beam Element. 6. Composite Plate and Shell Element. 7. Computational Statistics. 8. Nonlinear Analysis of Anisotropic Shells. 9. Programming Aspects. Appendices: A. Geometry of the Bema Element in Space. B. Contents of the Floppy Disk. Bibliography. Index.

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Book SynopsisA concise introductory course text on continuum mechanics Fundamentals of Continuum Mechanics focuses on the fundamentals of the subject and provides the background for formulation of numerical methods for large deformations and a wide range of material behaviours.Trade Review“Motivated students will benefit from this systematic, disciplined and concise treatment of the fundamentals of continuum mechanics. Many practitioners will also appreciate the logical organization, and the lucid descriptions of such matters as the distinctions between the various common stress and strain measures.” (Pure and Applied Geophysics, 1 November 2015) Table of ContentsPreface xiii Nomenclature xv Introduction 1 Part One Mathematical Preliminaries 3 1 Vectors 5 1.1 Examples 9 1.1.1 9 1.1.2 9 Exercises 9 Reference 11 2 Tensors 13 2.1 Inverse 15 2.2 Orthogonal Tensor 16 2.3 Principal Values 16 2.4 Nth-Order Tensors 18 2.5 Examples 18 2.5.1 18 2.5.2 18 Exercises 19 3 Cartesian Coordinates 21 3.1 Base Vectors 21 3.2 Summation Convention 23 3.3 Tensor Components 24 3.4 Dyads 25 3.5 Tensor and Scalar Products 27 3.6 Examples 29 3.6.1 29 3.6.2 29 3.6.3 29 Exercises 30 Reference 30 4 Vector (Cross) Product 31 4.1 Properties of the Cross Product 32 4.2 Triple Scalar Product 33 4.3 Triple Vector Product 33 4.4 Applications of the Cross Product 34 4.4.1 Velocity due to Rigid Body Rotation 34 4.4.2 Moment of a Force P about O 35 4.5 Non-orthonormal Basis 36 4.6 Example 37 Exercises 37 5 Determinants 41 5.1 Cofactor 42 5.2 Inverse 43 5.3 Example 44 Exercises 44 6 Change of Orthonormal Basis 47 6.1 Change of Vector Components 48 6.2 Definition of a Vector 50 6.3 Change of Tensor Components 50 6.4 Isotropic Tensors 51 6.5 Example 52 Exercises 53 Reference 56 7 Principal Values and Principal Directions 57 7.1 Example 59 Exercises 60 8 Gradient 63 8.1 Example: Cylindrical Coordinates 66 Exercises 67 Part Two Stress 69 9 Traction and Stress Tensor 71 9.1 Types of Forces 71 9.2 Traction on Different Surfaces 73 9.3 Traction on an Arbitrary Plane (Cauchy Tetrahedron) 75 9.4 Symmetry of the Stress Tensor 76 Exercise 77 Reference 77 10 Principal Values of Stress 79 10.1 Deviatoric Stress 80 10.2 Example 81 Exercises 82 11 Stationary Values of Shear Traction 83 11.1 Example: Mohr–Coulomb Failure Condition 86 Exercises 88 12 Mohr’s Circle 89 Exercises 93 Reference 93 Part Three Motion and Deformation 95 13 Current and Reference Configurations 97 13.1 Example 102 Exercises 103 14 Rate of Deformation 105 14.1 Velocity Gradients 105 14.2 Meaning of D 106 14.3 Meaning of W 108 Exercises 109 15 Geometric Measures of Deformation 111 15.1 Deformation Gradient 111 15.2 Change in Length of Lines 112 15.3 Change in Angles 113 15.4 Change in Area 114 15.5 Change in Volume 115 15.6 Polar Decomposition 116 15.7 Example 118 Exercises 118 References 120 16 Strain Tensors 121 16.1 Material Strain Tensors 121 16.2 Spatial Strain Measures 123 16.3 Relations Between D and Rates of EG and U 124 16.3.1 Relation Between Ė and D 124 16.3.2 Relation Between D and U 125 Exercises 126 References 128 17 Linearized Displacement Gradients 129 17.1 Linearized Geometric Measures 130 17.1.1 Stretch in Direction N 130 17.1.2 Angle Change 131 17.1.3 Volume Change 131 17.2 Linearized Polar Decomposition 132 17.3 Small-Strain Compatibility 133 Exercises 135 Reference 135 Part Four Balance of Mass, Momentum, and Energy 137 18 Transformation of Integrals 139 Exercises 142 References 143 19 Conservation of Mass 145 19.1 Reynolds’ Transport Theorem 148 19.2 Derivative of an Integral over a Time-Dependent Region 149 19.3 Example: Mass Conservation for a Mixture 150 Exercises 151 20 Conservation of Momentum 153 20.1 Momentum Balance in the Current State 153 20.1.1 Linear Momentum 153 20.1.2 Angular Momentum 154 20.2 Momentum Balance in the Reference State 155 20.2.1 Linear Momentum 156 20.2.2 Angular Momentum 157 20.3 Momentum Balance for a Mixture 158 Exercises 159 21 Conservation of Energy 161 21.1 Work-Conjugate Stresses 163 Exercises 165 Part Five Ideal Constitutive Relations 167 22 Fluids 169 22.1 Ideal Frictionless Fluid 169 22.2 Linearly Viscous Fluid 171 22.2.1 Non-steady Flow 173 Exercises 175 Reference 176 23 Elasticity 177 23.1 Nonlinear Elasticity 177 23.1.1 Cauchy Elasticity 177 23.1.2 Green Elasticity 178 23.1.3 Elasticity of Pre-stressed Bodies 179 23.2 Linearized Elasticity 182 23.2.1 Material Symmetry 183 23.2.2 Linear Isotropic Elastic Constitutive Relation 185 23.2.3 Restrictions on Elastic Constants 186 23.3 More Linearized Elasticity 187 23.3.1 Uniqueness of the Static Problem 188 23.3.2 Pressurized Hollow Sphere 189 Exercises 191 Reference 194 Index 195

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Book SynopsisPresents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer. The book features derivations of commonly used differential equations based on the fundamental continuum mechanical concepts encountered in various fields, such as engineering, physics, and geophysics. The book begins with geometric, algebraic, and analytical foundations before introducing topics in kinematics. The book then addresses balance laws, constitutive relations, and constitutive theory. Finally, the book presents an approach to multiconstituent continua based on mixture theory to illustrate how phenomena, such as diffusion and porous-Table of ContentsPreface v 1 Geometric Setting 1 1.1 Vectors and Euclidean Point Space 2 1.1.1 Vectors 2 1.1.2 Euclidean Point Space 6 1.1.3 Summary 8 1.2 Tensors 8 1.2.1 First-Order Tensors and Vectors 8 1.2.2 Second-Order Tensors 11 1.2.3 Cross Products, Triple Products, and Determinants 15 1.2.4 Orthogonal Tensors 20 1.2.5 Invariants of a Tensor 21 1.2.6 Derivatives of Tensor-Valued Functions 24 1.2.7 Summary 27 2 Kinematics I: The Calculus of Motion 29 2.1 Bodies, Motions, and Deformations 29 2.1.1 Deformation 32 2.1.2 Examples of Motions 33 2.1.3 Summary 36 2.2 Derivatives of Motion 36 2.2.1 Time Derivatives 37 2.2.2 Derivatives with Respect to Position 38 2.2.3 The Deformation Gradient 40 2.2.4 Summary 42 2.3 Pathlines, Streamlines, and Streaklines 43 2.3.1 Three Types of Arc 43 2.3.2 An Example 45 2.3.3 Summary 49 2.4 Integrals Under Motion 49 2.4.1 Arc, Surface, and Volume Integrals 49 2.4.2 Reynolds Transport Theorem 55 2.4.3 Summary 57 3 Kinematics II: Strain and its Rates 59 3.1 Strain 59 3.1.1 Symmetric Tensors 60 3.1.2 Polar Decomposition and the Deformation Gradient 64 3.1.3 Examples 66 3.1.4 Cauchy–Green and Strain Tensors 68 3.1.5 Strain Invariants 70 3.1.6 Summary 71 3.2 Infinitesimal Strain 72 3.2.1 The Infinitesimal Strain Tensor 72 3.2.2 Summary 75 3.3 Strain Rates 75 3.3.1 Stretching and Spin Tensors 76 3.3.2 Skew Tensors, Spin, and Vorticity 79 3.3.3 Summary 84 3.4 Vorticity and Circulation 84 3.4.1 Circulation 84 3.4.2 Summary 88 3.5 Observer Transformations 89 3.5.1 Changes in Frame of Reference 89 3.5.2 Summary 95 4 Balance Laws 97 4.1 Mass Balance 98 4.1.1 Local Forms of Mass Balance 99 4.1.2 Summary 102 4.2 Momentum Balance 102 4.2.1 Analysis of Stress 104 4.2.2 Inertial Frames of Reference 110 4.2.3 Momentum Balance in Referential Coordinates 113 4.2.4 Summary 114 4.3 Angular Momentum Balance 115 4.3.1 Symmetry of the Stress Tensor 117 4.3.2 Summary 118 4.4 Energy Balance 119 4.4.1 Thermal Energy Balance 122 4.4.2 Summary 124 4.5 Entropy Inequality 124 4.5.1 Motivation 125 4.5.2 Clausius–Duhem Inequality 126 4.5.3 Summary 127 4.6 Jump Conditions 127 4.6.1 Singular Surfaces 129 4.6.2 Localization 132 4.6.3 Summary 135 5 Constitutive Relations: Examples of Mathematical Models 137 5.1 Heat Transfer 138 5.1.1 Properties of the Heat Equation 140 5.1.2 Summary 142 5.2 Potential Theory 143 5.2.1 Motivation 143 5.2.2 Boundary Conditions 144 5.2.3 Uniqueness of Solutions to the Poisson Equation 146 5.2.4 Maximum Principle 147 5.2.5 Mean Value Property 150 5.2.6 Summary 151 5.3 Fluid Mechanics 152 5.3.1 Ideal Fluids 152 5.3.2 An Ideal Fluid in a Rotating Frame of Reference 154 5.3.3 Acoustics 155 5.3.4 Incompressible Newtonian Fluids 158 5.3.5 Stokes Flow 159 5.3.6 Summary 163 5.4 Solid Mechanics 164 5.4.1 Static Displacements 164 5.4.2 Elastic Waves 167 5.4.3 Summary 170 6 Constitutive Theory 173 6.1 Conceptual Setting 174 6.1.1 The Need to Close the System 174 6.1.2 Summary 176 6.2 Determinism and Equipresence 177 6.2.1 Determinism 177 6.2.2 Equipresence 177 6.2.3 Summary 178 6.3 Objectivity 179 6.3.1 Reducing Functional Dependencies 180 6.3.2 Summary 182 6.4 SYMMETRY 183 6.4.1 Changes in Reference Configuration 183 6.4.2 Symmetry Groups 186 6.4.3 Classification of Materials 189 6.4.4 Implications for Thermoviscous Fluids 193 6.4.5 Summary 193 6.5 Admissibility 194 6.5.1 Implications of the Entropy Inequality 195 6.5.2 Analysis of Equilibrium 197 6.5.3 Linear, Isotropic, Thermoelastic Solids 199 6.5.4 Summary 202 7 Multiconstituent Continua 203 7.1 Constituents 204 7.1.1 Configurations and Motions 204 7.1.2 Volume Fractions and Densities 206 7.1.3 Summary 208 7.2 Multiconstituent Balance Laws 209 7.2.1 Multiconstituent Mass Balance 210 7.2.2 Multiconstituent Momentum Balance 212 7.2.3 Multiconstituent Angular Momentum Balance 214 7.2.4 Multiconstituent Energy Balance 215 7.2.5 Multiconstituent Entropy Inequality 216 7.2.6 Isothermal, Nonreacting Multiphase Mixtures 217 7.2.7 Summary 219 7.3 Fluid Flow in a Porous Solid 220 7.3.1 Modeling Assumptions for Porous Media 221 7.3.2 Balance Laws for the Fluid and Solid Phases 223 7.3.3 Equilibrium Constraints 225 7.3.4 Linear Extensions From Equilibrium 226 7.3.5 Commentary 228 7.3.6 Potential Formulation of Darcy’s Law 229 7.3.7 Summary 233 7.4 Diffusion in a Binary Fluid Mixture 234 7.4.1 Modeling Assumptions for Binary Diffusion 235 7.4.2 Balance Laws for the Two Species 235 7.4.3 Constitutive Relationships for Diffusion 236 7.4.4 Modeling Solute Transport 239 7.4.5 Summary 242 A Guide to Notation 243 A.1 General Conventions 243 A.2 Letters Reserved for Dedicated Uses 244 A.3 Special Symbols 245 B Vector Integral Theorems 247 B.1 Stokes’s Theorem 248 B.2 The Divergence Theorem 249 B.3 The Change-of-variables Theorem 252 C Hints and Solutions to Exercises 253 References 265 Index 269

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Book SynopsisProcess machines are critical to the profitability of processes. Safe, efficient and reliable machines are required to maintain dependable manufacturing processes that can create saleable, on-spec product on time, and at the desired production rate. As the wards of process machinery, we wish to keep our equipment in serviceable condition. One of the most challenging aspects of a machinery professional or operator''s job is deciding whether an operating machine should be shut down due to a perceived problem or be allowed to keep operating. If he or she wrongly recommends a repair be conducted, the remaining useful machine life is wasted, but if he or she is right, they can save the organization from severe consequences, such as product releases, fires, costly secondary machine damage, etc. This economic balancing act is at the heart of all machinery assessments. Troubleshooting is part science and part art. Simple troubleshooting tables or decision trees are rarely effeTable of ContentsPreface xi Acknowledgements xv 1 Troubleshooting for Fun and Profit 1 1.1 Why Troubleshoot? 10 1.2 Traits of a Successful Troubleshooter 13 2 An Insight in Design: Machines and Their Components Serve a Function 19 2.1 An Overview of the Design Process 30 2.2 Complex Machine Element Environments 34 3 Machinery Design Issues and Failure Modes 37 3.1 Common Failure Modes 44 3.1.1 Pluggage 45 3.1.2 Erosive Wear 45 3.1.3 Fatigue 46 3.1.4 Compressor Blade Fatigue Example 47 3.1.5 Bearing Failure 49 3.1.6 Rubbing 50 3.1.7 Unique Failure Modes 50 4 Machinery in Process Services – The Big Picture 53 5 Causes Versus Symptoms 61 5.1 Causal Chains 66 5.2 Summary 71 6 Approach Field Troubleshooting Like a Reputable News Reporter 73 7 The “What” Questions 77 7.1 What is the Problem or What Are the Symptoms? 78 7.2 What Is Your Assessment of the Problem? 80 7.3 What Is at Stake? 85 7.4 What Risk Is at Hand? 86 7.5 What Additional Information Is Required? 87 8 Who Knows the Most About the Problem? 91 9 When Do the Symptoms Show Up? 97 9.1 “When” Questions to Ask 100 9.2 Ways to Display Time Related Data 101 9.3 Timelines 102 9.4 Trend Plots 106 9.5 Constant Amplitude Trends 110 9.6 Step Changes 110 9.7 Gradual Versus Rapidly Changing Trends 111 9.8 Correlations 113 9.9 Speed-Related Issues 114 9.10 Erratic Amplitude 117 10 Where Do the Symptoms Show Up? 121 10.1 Locating a Machine-Train Problem 122 10.2 Troubleshooting Problems Involving Multiple Machine-Trains 128 10.3 Multiple Versus Single Machine Train Examples 130 10.4 Analyzing Noises, Pings, and Knocks 132 10.5 Seeing the Light at the End of the Tunnel 135 11 Why Is the Problem Occurring? 137 11.1 Fitting the Pieces Together 139 11.2 Reciprocating Compressor Example 142 11.3 Troubleshooting Matrices 143 11.4 Assessing Machine with Multiple Symptoms 144 12 Analyze, Test, Act, and Confirm (Repeat as Needed) 147 12.1 The Iterative Path to the Final Solution 150 13 Real-World Examples 155 13.1 Case Study #1 155 13.1.1 Closing Comments 158 13.2 Case Study #2 158 13.2.1 Closing Comments 163 13.3 Case Study #3 163 13.3.1 Closing Comments 170 13.4 Case Study #4 170 13.5 Case Study #5 174 13.5.1 Closing Comments 179 14 The “Hourglass” Approach to Troubleshooting 181 14.1 Thinking and Acting Globally 186 15 Vibration Analysis 187 15.1 Vibration Analysis Primer 188 15.2 Identifying Machine Vibration Characteristics 201 16 Applying the 5Qs to Rotordynamic Investigations 207 16.1 Introduction 208 16.1.1 Rotordynamics: A Brief Overview 208 16.2 Using Rotordynamic Results for Troubleshooting 213 16.3 Closing 222 17 Managing Critical Machinery Vibration Data 227 17.1 Vibration Analysis Strategies 230 18 Closing Remarks 235 18.1 Practice the Method 235 18.2 Provide Training on Fault Trees and Cause Mapping 236 18.3 Employ Team Approach for Complex Problems 236 18.4 Get Management’s Support 237 Appendix A: The Field Troubleshooting Process—Step by Step 239 Appendix B: Troubleshooting Matrices and Tables 249 Index 351

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Book SynopsisThe Advances in Chemical Physics series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. This is the only series of volumes available that presents the cutting edge of research in chemical physics.Table of ContentsList of Contributors Volume 162 IX Preface to the Series XI ELECTRONIC STRUCTURE AND DYNAMICS OF SINGLET FISSION IN ORGANIC MOLECULES AND CRYSTALS 1Timothy C. Berkelbach AN APPROACH TO “QUANTUMNESS” IN COHERENT CONTROL 39Torsten Scholak and Paul Brumer ENERGETIC AND NANOSTRUCTURAL DESIGN OF SMALL-MOLECULAR-TYPE ORGANIC SOLAR CELLS 137Masahiro Hiramoto SINGLE MOLECULE DATA ANALYSIS: AN INTRODUCTION 205Meysam Tavakoli, J. Nicholas Taylor, Chun-Biu Li,Tamiki Komatsuzaki, and Steve Pressé CHEMISTRY WITH CONTROLLED IONS 307Stefan Willitsch Index 341

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Book SynopsisA revised edition to applied gas dynamics with exclusive coverage on jets and additional sets of problems and examples The revised and updated second edition of Applied Gas Dynamics offers an authoritative guide to the science of gas dynamics. Written by a noted expert on the topic, the text contains a comprehensive review of the topic; from a definition of the subject, to the three essential processes of this science: the isentropic process, shock and expansion process, and Fanno and Rayleigh flows. In this revised edition, there are additional worked examples that highlight many concepts, including moving shocks, and a section on critical Mach number is included that helps to illuminate the concept. The second edition also contains new exercise problems with the answers added. In addition, the information on ram jets is expanded with helpful worked examples. It explores the entire spectrum of the ram jet theory and includes a set of exercise problems to aid in the understanding ofTable of ContentsPreface xv Author Biography xvii About the Companion Website xix 1 Basic Facts 1 1.1 Definition of Gas Dynamics 1 1.2 Introduction 1 1.3 Compressibility 2 1.3.1 Limiting Conditions for Compressibility 3 1.4 Supersonic Flow – What is it? 4 1.5 Speed of Sound 5 1.6 Temperature Rise 7 1.7 Mach Angle 8 1.7.1 Small Disturbance 10 1.7.2 Finite Disturbance 10 1.8 Thermodynamics of Fluid Flow 11 1.9 First Law of Thermodynamics (Energy Equation) 11 1.9.1 Energy Equation for an Open System 12 1.9.2 Adiabatic Flow Process 14 1.10 The Second Law of Thermodynamics (Entropy Equation) 15 1.11 Thermal and Calorical Properties 16 1.11.1 Thermally Perfect Gas 16 1.12 The Perfect Gas 17 1.12.1 Entropy Calculation 18 1.12.2 Isentropic Relations 20 1.12.3 Limitations on Air as a Perfect Gas 25 1.13 Wave Propagation 26 1.14 Velocity of Sound 26 1.15 Subsonic and Supersonic Flows 27 1.16 Similarity Parameters 28 1.17 Continuum Hypothesis 28 1.18 Compressible Flow Regimes 30 1.19 Summary 31 Exercise Problems 34 2 Steady One-Dimensional Flow 43 2.1 Introduction 43 2.2 Fundamental Equations 43 2.3 Discharge from a Reservoir 45 2.3.1 Mass Flow Rate per Unit Area 47 2.3.2 Critical Values 51 2.4 Streamtube Area–Velocity Relation 54 2.5 de Laval Nozzle 57 2.5.1 Mass Flow Relation in Terms of Mach Number 65 2.5.2 Maximum Mass Flow Rate per Unit Area 65 2.6 Supersonic Flow Generation 66 2.6.1 Nozzles 68 2.6.2 Physics of the Nozzle Flow Process 69 2.7 Performance of Actual Nozzles 71 2.7.1 Nozzle Efficiency 71 2.7.2 Nozzle Discharge Coefficient 73 2.8 Diffusers 75 2.8.1 Special Features of Supersonic Diffusers 77 2.8.2 Supersonic Wind Tunnel Diffusers 78 2.8.3 Supersonic Inlets 81 2.8.4 Fixed-Geometry Inlet 82 2.8.5 Variable-Geometry Inlet 83 2.8.6 Diffuser Efficiency 84 2.9 Dynamic Head Measurement in Compressible Flow 88 2.9.1 Compressibility Correction to Dynamic Pressure 91 2.10 Pressure Coefficient 95 2.11 Summary 97 Exercise Problems 99 3 Normal Shock Waves 113 3.1 Introduction 113 3.2 Equations of Motion for a Normal Shock Wave 113 3.3 The Normal Shock Relations for a Perfect Gas 115 3.4 Change of Stagnation or Total Pressure Across a Shock 118 3.5 Hugoniot Equation 121 3.5.1 Moving Shocks 123 3.6 The Propagating Shock Wave 123 3.6.1 Weak Shock 128 3.6.2 Strong Shock 130 3.7 Reflected Shock Wave 133 3.8 Centered Expansion Wave 138 3.9 Shock Tube 139 3.9.1 Shock Tube Applications 142 3.10 Summary 145 Exercise Problems 148 4 Oblique Shock and Expansion Waves 155 4.1 Introduction 155 4.2 Oblique Shock Relations 156 4.3 Relation Between 𝛽 and 𝜃 158 4.4 Shock Polar 160 4.5 Supersonic Flow Over a Wedge 162 4.6 Weak Oblique Shocks 165 4.7 Supersonic Compression 167 4.8 Supersonic Expansion by Turning 169 4.9 The Prandtl–Meyer Expansion 170 4.9.1 Velocity Components Vr and V𝜙 172 4.9.2 The Prandtl–Meyer Function 175 4.9.3 Compression 177 4.10 Simple and Nonsimple Regions 178 4.11 Reflection and Intersection of Shocks and Expansion Waves 178 4.11.1 Intersection of Shocks of the Same Family 181 4.11.2 Wave Reflection from a Free Boundary 183 4.12 Detached Shocks 189 4.13 Mach Reflection 191 4.14 Shock-Expansion Theory 197 4.15 Thin Airfoil Theory 202 4.15.1 Application of Thin Aerofoil Theory 203 4.16 Summary 210 Exercise Problems 212 5 Compressible Flow Equations 221 5.1 Introduction 221 5.2 Crocco’s Theorem 221 5.2.1 Basic Solutions of Laplace’s Equation 224 5.3 General Potential Equation for Three-Dimensional Flow 225 5.4 Linearization of the Potential Equation 226 5.4.1 Small Perturbation Theory 227 5.5 Potential Equation for Bodies of Revolution 229 5.5.1 Conclusions 230 5.5.2 Solution of Nonlinear Potential Equation 231 5.6 Boundary Conditions 231 5.6.1 Bodies of Revolution 232 5.7 Pressure Coefficient 233 5.7.1 Bodies of Revolution 234 5.8 Summary 234 Exercise Problems 237 6 Similarity Rule 239 6.1 Introduction 239 6.2 Two-Dimensional Flow: The Prandtl–Glauert Rule for Subsonic Flow 239 6.2.1 Prandtl–Glauert Transformations 239 6.2.2 The Direct Problem (Version I) 241 6.2.3 The Indirect Problem (Case of Equal Potentials): P–G Transformation (Version II) 243 6.2.4 Streamline Analogy (Version III): Gothert’s Rule 244 6.3 Prandtl–Glauert Rule for Supersonic Flow: Versions I and II 245 6.3.1 Subsonic Flow 246 6.3.2 Supersonic Flow 246 6.4 The von Karman Rule for Transonic Flow 248 6.4.1 Use of the von Karman Rule 249 6.5 Hypersonic Similarity 250 6.6 Three-Dimensional Flow: Gothert’s Rule 252 6.6.1 General Similarity Rule 252 6.6.2 Gothert’s Rule 254 6.6.3 Application toWings of Finite Span 255 6.6.4 Application to Bodies of Revolution and Fuselages 255 6.6.5 The Prandtl–Glauert Rule 257 6.6.6 The von Karman Rule for Transonic Flow 261 6.7 Critical Mach Number 261 6.7.1 Calculation of M∗∞ 264 6.8 Summary 266 Exercise Problems 269 7 Two-Dimensional Compressible Flows 271 7.1 Introduction 271 7.2 General Linear Solution for Supersonic Flow 271 7.2.1 Existence of Characteristics in a Physical Problem 273 7.2.2 Equation for the Streamlines from Kinematic Flow Condition 274 7.3 Flow over a Wave-Shaped Wall 276 7.3.1 Incompressible Flow 276 7.3.2 Compressible Subsonic Flow 277 7.3.3 Supersonic Flow 278 7.3.4 Pressure Coefficient 278 7.4 Summary 280 Exercise Problems 280 8 Flow with Friction and Heat Transfer 283 8.1 Introduction 283 8.2 Flow in Constant Area Duct with Friction 283 8.2.1 The Fanno Line 284 8.3 Adiabatic, Constant-Area Flow of a Perfect Gas 285 8.3.1 Definition of Friction Coefficient 286 8.3.2 Effects of Wall Friction on Fluid Properties 287 8.3.3 Second Law of Thermodynamics 288 8.3.4 Working Relations 289 8.4 Flow with Heating or Cooling in Ducts 294 8.4.1 Governing Equations 294 8.4.2 Simple-Heating Relations for a Perfect Gas 295 8.5 Summary 300 Exercise Problems 303 9 Method of Characteristics 309 9.1 Introduction 309 9.2 The Concepts of Characteristics 309 9.3 The Compatibility Relation 310 9.4 The Numerical Computational Method 312 9.4.1 Solid and Free Boundary Points 313 9.4.2 Sources of Error 316 9.4.3 Axisymmetric Flow 316 9.4.4 Nonisentropic Flow 317 9.5 Theorems for Two-Dimensional Flow 318 9.6 Numerical Computation with Weak Finite Waves 320 9.6.1 Reflection of Waves 320 9.7 Design of Supersonic Nozzle 323 9.7.1 Contour Design Details 324 9.8 Summary 328 10 Measurements in Compressible Flow 329 10.1 Introduction 329 10.2 Pressure Measurements 329 10.2.1 Liquid Manometers 329 10.2.2 Measuring Principle of Manometers 330 10.2.3 Dial-Type Pressure Gauges 332 10.2.4 Pressure Transducers 333 10.3 Temperature Measurements 335 10.4 Velocity and Direction 338 10.5 Density Problems 339 10.6 Compressible Flow Visualization 339 10.6.1 Supersonic Flows 340 10.7 Interferometer 341 10.7.1 Formation of Interference Patterns 341 10.7.2 Quantitative Evaluation 342 10.7.3 Fringe-Displacement Method 344 10.8 Schlieren System 344 10.8.1 Range and Sensitivity of the Schlieren System 347 10.8.2 Optical Components Quality Requirements 347 10.8.3 Sensitivity of the Schlieren Method for Shock and Expansion Studies 350 10.9 Shadowgraph 352 10.9.1 Comparison of the Schlieren and Shadowgraph Methods 353 10.10 Wind Tunnels 354 10.10.1 High-SpeedWind Tunnels 354 10.10.2 Blowdown TypeWind Tunnels 354 10.10.3 Induction Type Tunnels 355 10.10.4 Continuous Supersonic Wind Tunnels 356 10.10.5 Losses in Supersonic Tunnels 357 10.10.6 Supersonic Wind Tunnel Diffusers 358 10.10.7 Effects of Second Throat 360 10.10.8 Compressor Tunnel Matching 362 10.10.9 The Mass Flow Rate 365 10.10.10 Blowdown Tunnel Operation 369 10.10.11 Optimum Conditions 372 10.10.12 Running Time of Blowdown Wind Tunnels 373 10.11 Hypersonic Tunnels 375 10.11.1 Hypersonic Nozzle 377 10.12 Instrumentation and Calibration ofWind Tunnels 380 10.12.1 Calibration of SupersonicWind Tunnels 380 10.12.2 Calibration 381 10.12.3 Mach Number Determination 381 10.12.4 Pitot Pressure Measurement 382 10.12.5 Static Pressure Measurement 382 10.12.6 Determination of Flow Angularity 383 10.12.7 Determination of Turbulence Level 383 10.12.8 Determination of Test-Section Noise 384 10.12.9 Use of Calibration Results 384 10.12.10 Starting of Supersonic Tunnels 384 10.12.11 Starting Loads 385 10.12.12 Reynolds Number Effects 385 10.12.13 Model Mounting-Sting Effects 385 10.13 Calibration and Use of Hypersonic Tunnels 386 10.13.1 Calibration of Hypersonic Tunnels 386 10.13.2 Mach Number Determination 386 10.13.3 Determination of Flow Angularity 388 10.13.4 Determination of Turbulence Level 388 10.13.5 Reynolds Number Effects 389 10.13.6 Force Measurements 389 10.14 Flow Visualization 390 10.15 Summary 390 Exercise Problems 393 11 Ramjet 395 11.1 Introduction 395 11.2 The Ideal Ramjet 396 11.3 Aerodynamic Losses 401 11.4 Aerothermodynamics of Engine Components 404 11.4.1 Engine Inlets 404 11.5 Flow Through Inlets 405 11.5.1 Inlet Flow Process 406 11.5.2 Boundary Layer Separation 406 11.5.3 Flow Over the Inlet 406 11.6 Performance of Actual Intakes 410 11.6.1 Isentropic Efficiency 410 11.6.2 Stagnation Pressure Ratio 411 11.6.3 Supersonic Inlets 411 11.6.4 Supersonic Diffusers 412 11.6.5 Starting Problem 413 11.7 Shock–Boundary Layer Interaction 418 11.8 Oblique Shock Wave Incident on Flat Plate 419 11.9 Normal Shocks in Ducts 420 11.10 External Supersonic Compression 422 11.11 Two-Shock Intakes 423 11.12 Multi-Shock Intakes 427 11.13 Isentropic Compression 429 11.14 Limits of External Compression 431 11.15 External Shock Attachment 433 11.16 Internal Shock Attachment 433 11.17 Pressure Loss 434 11.18 Supersonic Combustion 442 11.19 Summary 444 Exercise Problems 447 12 Jets 451 12.1 Introduction 451 12.1.1 Subsonic Jets 453 12.2 Mathematical Treatment of Jet Profiles 454 12.3 Theory of Turbulent Jets 455 12.3.1 Mean Velocity and Mean Temperature 456 12.3.2 Turbulence Characteristics of Free Jets 457 12.3.3 Mixing Length 458 12.4 Experimental Methods for Studying Jets and the Techniques Used for Analysis 461 12.4.1 Pressure Measurement 462 12.5 Expansion Levels of Jets 464 12.5.1 Overexpanded Jets 464 12.5.2 Correctly Expanded Jets 467 12.5.3 Underexpanded Jets 469 12.6 Control of Jets 471 12.6.1 Classification of Control Methods 473 12.6.2 Role of Shear Layer in Flow Control 474 12.6.3 Supersonic Shear Layers 475 12.6.4 Use of Tabs for Jet Control 477 12.6.5 Evaluation of the Effectiveness of Some Specific Passive Controls 481 12.6.6 Grooves and Cutouts 519 12.7 Noncircular Jets and Shifted Tabs 519 12.7.1 Jet Control with Tabs 523 12.7.2 Shifted Tabs 527 12.7.3 Ventilated Triangular Tabs 532 12.7.4 Tab Edge Effect 535 12.8 Summary 541 Appendix A 547 References 619 Index 625

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Trade Review“This hefty tome offers a comprehensive introduction to fluid dynamics, mainly with application to planetary science and astrophysics in mind. ... it is a useful resource for course development. It certainly offers a wealth of interesting insights into fluid dynamics and plasma physics for those with experience, and I found it to be an enjoyable and informative read.” (David A. Burton, The Observatory, Vol. 137 (1260), October, 2017)“Modern Fluid Dynamics for Physics and Astrophysics is a welcome addition that helps fill the gap between introductory and advanced books. … The textbook is especially suited for graduate courses, but I believe that it can also be easily used for senior undergraduate courses. … Modern Fluid Dynamics for Physics and Astrophysics to be a very good resource, not just for astrophysics and geophysics courses but for any physics course that covers the fundamental topic of fluid dynamics.” (Giuseppe Lodato, Physics Today, May, 2017)Table of Contents

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Book SynopsisThe Mathematical Elasticity set contains three self-contained volumes that together provide the only modern treatise on elasticity. They introduce contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. An extended preface and extensive bibliography have been added to each volume to highlight the progress that has been made since the original publication.The first book, Three-Dimensional Elasticity, covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. In volume two, Theory of Plates, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. The objective of Theory of Shells, the final volume, is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural.These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

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Book SynopsisClassical Mechanics, a branch of physics that addresses the motion of macroscopic objects, is founded upon fundamental principles that govern the behavior of physical bodies. Central to this are Newton's three laws of motion. The first law, or the law of inertia, posits that an object will remain in a state of rest or uniform motion unless acted upon by an external force. The second law provides a mathematical description of how the velocity of an object changes when it is subjected to an external force, and is often expressed as F=ma, where F is the total force, m is the object's mass, and a is its acceleration. The third law, the principle of action and reaction, asserts that for every action, there is an equal and opposite reaction. These laws have been instrumental in the development of various disciplines such as engineering and astronomy and remain applicable to most physical systems, except when dealing with phenomena at extremely small scales or relativistic speeds. The Fundamentals of Motion: Introduction to Classical Mechanics is an essential textbook that provides a thorough examination of the principles underlying the motion of macroscopic objects. Designed for students, educators, and professionals in physics and engineering, this book delves into the core concepts of Classical Mechanics, including Newton's laws of motion, conservation of momentum and energy, dynamics, kinematics, and rotational motion. It offers a systematic approach to understanding fundamental theories and mathematical formulations, coupled with illustrative examples and practical exercises. This textbook also incorporates discussions on the historical development and philosophical aspects of Classical Mechanics, the limitations of the classical view in the face of relativistic and quantum phenomena, and emerging connections to other areas of physics. With its methodical exposition and clear insights, Fundamentals of Motion: Introduction to Classical Mechanics serves as an indispensable guide for those seeking to understand the intricate workings of physical laws that govern our world, equipping readers with the knowledge and tools to explore the underlying nature of motion and mechanics.

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Book SynopsisThe formalism processing of unbuckled solids mechanics involves several mathematical tools which are to be mastered at the same time. This volume collects the main points which take place in the course of the formalism, so that the user immediately finds what he needs without looking for it. Furthermore, the book contains a methodological formulary to guide the user in his approach.Table of ContentsIntroduction xi Table of Notations xiii Chapter 1. Vector Calculus 1 1.1. Vector space 1 1.1.1. Definition 1 1.1.2. Vector space – dimension – basis 2 1.1.3. Affine space 3 1.2. Affine space of dimension 3 – free vector 4 1.3. Scalar product a⋅b 5 1.3.1. Properties of the scalar product 6 1.3.2. Scalar square – unit vector 6 1.3.3. Geometric interpretation of the scalar product 7 1.3.4. Solving the equation a�� ⋅ x�� = 0 9 1.4. Vector product a ∧ b 9 1.4.1. Definition 9 1.4.2. Geometric interpretation of the vector product 10 1.4.3. Properties of vector product 11 1.4.4. Solving the equation a ∧ x = b 11 1.5. Mixed product (a ,b, c ) 12 1.5.1. Definition 12 1.5.2. Geometric interpretation of the mixed product 12 1.5.3. Properties of the mixed product 13 1.6. Vector calculus in the affine space of dimension 3 15 1.6.1. Orthonormal basis 15 1.6.2. Analytical expression of the scalar product 16 1.6.3. Analytical expression of the vector product 16 1.6.4. Analytical expression of the mixed product 17 1.7. Applications of vector calculus 18 1.7.1. Double vector product 18 1.7.2. Resolving the equation a�� ⋅ x�� = b 22 1.7.3. Resolving the equation a ∧ x = b 23 1.7.4. Equality of Lagrange 25 1.7.5. Equations of planes 25 1.7.6. Relations within the triangle 27 1.8. Vectors and basis changes 28 1.8.1. Einstein’s convention 28 1.8.2. Transition table from basis (e) to basis (E) 30 1.8.3. Characterization of the transition table 32 Chatper 2. Torsors and Torsor Calculus 35 2.1. Vector sets 35 2.1.1. Discrete set of vectors 35 2.1.2. Set of vectors defined on a continuum 36 2.2. Introduction to torsors 37 2.2.1. Definition 37 2.2.2. Equivalence of vector families 38 2.3. Algebra torsors 38 2.3.1. Equality of two torsors 38 2.3.2. Linear combination of torsors 39 2.3.3. Null torsors 39 2.3.4. Opposing torsor 40 2.3.5. Product of two torsors 40 2.3.6. Scalar moment of a torsor – equiprojectivity 41 2.3.7. Invariant scalar of a torsor 43 2.4. Characterization and classification of torsors 43 2.4.1. Torsors with a null resultant 43 2.4.2. Torsors with a no-null resultant 45 2.5. Derivation torsors 48 2.5.1. Torsor dependent on a single parameter q 49 2.5.2. Torsor dependent of n parameters qi functions of p 51 2.5.3. Explicitly dependent torsor of n + 1 parameters 52 Chapter 3. Derivation of Vector Functions 55 3.1. Derivative vector: definition and properties 55 3.2. Derivative of a function in a basis 56 3.3. Deriving a vector function of a variable 57 3.3.1. Relations between derivatives of a function in different bases 57 3.3.2. Differential form associated with two bases 63 3.4. Deriving a vector function of two variables 65 3.5. Deriving a vector function of n variables 68 3.6. Explicit intervention of the variable p 70 3.7. Relative rotation rate of a basis relative to another 71 Chapter 4. Vector Functions of One Variable Skew Curves 73 4.1. Vector function of one variable 73 4.2. Tangent at a point M 74 4.3. Unit tangent vector τ ( q) 76 4.4. Main normal vector ( ) q ν 77 4.5. Unit binormal vector ( ) q β 79 4.6. Frenet’s basis 80 4.7. Curvilinear abscissa 81 4.8. Curvature, curvature center and curvature radius 83 4.9. Torsion and torsion radius 84 4.10. Orientation in (λ) of the Frenet basis 87 Chapter 5. Vector Functions of Two Variables Surfaces 91 5.1. Representation of a vector function of two variables 91 5.1.1. Coordinate curves 91 5.1.2. Regular or singular point – tangent plane – unit normal vector 93 5.1.3. Distinctive surfaces 95 5.1.4. Ruled surfaces 101 5.1.5. Area element 110 5.2. General properties of surfaces 111 5.2.1. First quadratic form 111 5.2.2. Darboux–Ribaucour’s trihedral 114 5.2.3. Second quadratic form 119 5.2.4. Meusnier’s theorems 121 5.2.5. Geodesic torsion 123 5.2.6. Prominent curves traced on a surface 125 5.2.7. Directions and principal curvatures of a surface 127 Chapter 6. Vector Function of Three Variables: Volumes 135 6.1. Vector functions of three variables 135 6.1.1. Coordinate surfaces 135 6.1.2. Coordinate curves 136 6.1.3. Orthogonal curvilinear coordinates 136 6.2. Volume element 137 6.2.1. Definition 137 6.2.2. Applications to traditional coordinate systems 138 6.3. Rotation rate of the local basis 139 6.3.1. Calculation of the partial rotation rate 1δ (λ ,e) 140 6.3.2. Calculation of the rotation rate 143 Chapter 7. Linear Operators 145 7.1. Definition 145 7.2. Intrinsic properties 145 7.3. Algebra of linear operators 147 7.3.1. Unit operator 147 7.3.2. Equality of two linear operators 147 7.3.3. Product of a linear operator by a scalar 147 7.3.4. Sum of two linear operators 148 7.3.5. Multiplying two linear operators 148 7.4. Bilinear form 149 7.5. Quadratic form 150 7.6. Linear operator and basis change 150 7.7. Examples of linear operators 152 7.7.1. Operation f = a ^ F 152 7.7.2. Operation f = a ^ (a ^ F) 152 7.7.3. Operation f = a(b ⋅ F) 153 7.7.4. Operation f = a ^ (F ^ a) 155 7.8. Vector rotation Ru��,a 156 7.8.1. Expression of the vector rotation 156 7.8.2. Quaternion associated with the vector rotation Ru��,a 159 7.8.3. Matrix representation of the vector rotation 160 7.8.4. Basis change and rotation vector 162 Chapter 8. Homogeneity and Dimension 165 8.1. Notion of homogeneity 165 8.2. Dimension 165 8.3. Standard mechanical dimensions 166 8.4. Using dimensional equations 168 Bibliography 171 Index 173

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Book SynopsisFluid mechanics is an important scientific field with various industrial applications for flows or energy consumption and efficiency issues. This book has as main aim to be a textbook of applied knowledge in real fluids as well as to the Hydraulic systems components and operation, with emphasis to the industrial or real life problems for piping and aerodynamic design geometries. Various problems will be presented and analyzed through this book. Table of ContentsPreface ix Chapter 1. Pipe Networks 1 1.1. Introduction 1 1.2. Calculation of pipe networks 3 1.3. Problem-solving methodology for pipe networks 10 1.4. Overall approach for the network calculation 12 1.5. The Hazen–Williams equation for network analysis 13 1.6. Hazen–Williams and Darcy–Weisbach identity 15 1.7. Hardy–Cross method 18 1.8. Formulae 21 1.9. Questions 23 1.10. Problems with solutions 23 1.11. Problems to be solved 53 Chapter 2. Open Channel Flow 57 2.1. Introduction 57 2.2. Non-dimensional parameters in open channels 58 2.3. Open channel types of flow 59 2.4. Open channels’ geometrical shapes 61 2.4.1. Channels of rectangular cross-sectional area 61 2.4.2. Channels of trapezoidal cross-sectional area 62 2.4.3. Channels of circular cross-sectional area 63 2.5. The hydraulic jump 65 2.6. Calculation of the depth flow after the hydraulic jump 65 2.7. Velocity distribution 68 2.8. Velocity distribution at the vertical level 68 2.9. Uniform flow in open channel equations – Chezy type 70 2.10. Best hydraulic cross-sectional area 75 2.11. Specific flow energy 79 2.12. Channels of rectangular cross-sectional area 80 2.13. Open channels’ more adequate cross-sectional areas 83 2.13.1. Rectangular cross-sectional area 83 2.13.2. Trapezoidal cross-sectional area 85 2.14. Non-uniform flow in open channels 88 2.15. Channels of non-rectangular cross-section area 90 2.16. Formulae 92 2.16.1. Channels of rectangular cross-sectional area formulae 93 2.16.2. Channels of trapezoidal cross-section formulae 93 2.16.3. Channels of circular cross-sectional area formulae 94 2.16.4. Channels of rectangular cross-sectional area formulae 99 2.16.5. Channels of non-rectangular cross-sectional area formulae 100 2.17. Questions 101 2.18. Problems with solutions 103 2.19. Problems to be solved 116 Chapter 3. Boundary Layer 119 3.1. Introduction 119 3.2. Laminar incompressible boundary layer 120 3.3. Characteristic values of the boundary layer 125 3.3.1. Thickness δ of the boundary layer 125 3.3.2. The thickness displacement 1 δ1’.126 3.4. Flow types in the boundary layer 127 3.5. Formulae 131 3.6. Questions 133 3.7. Problems with solutions 133 3.8. Problems to be solved 145 Chapter 4. Flow Around Solid Bodies 147 4.1. Introduction 147 4.2. Geometrical characteristics of an airfoil 148δ 4.3. Kutta–Joukowski equation 150 4.4. Aerodynamic paradox 152 4.5. Pressure distribution in an airfoil 153 4.6. Lift curve 156 4.7. Drag force and drag coefficient curve 158 4.7.1. Drag of skin friction 158 4.7.2. Form drag 159 4.7.3. Induced drag 161 4.8. Parameters that influence the drag coefficient CD 163 4.8.1. Dependence of CD on the body’s shape 163 4.8.2. Dependence of CD on relative roughness 165 4.8.3. Dependence of CD on the Reynolds number 170 4.9. External flow around industrial solid bodies 177 4.9.1. Car’s motion 177 4.9.2. Surface vessel’s motion 178 4.9.3. Wind flow in ground constructions 179 4.9.4. Airplane’s motion 181 4.10. Drag in fluid drops and gas bubbles in creeping flow 190 4.11. Formulae 191 4.12. Questions 193 4.13. Problems with solutions 196 4.14. Problems to be solved 209 Appendices 211 Appendix 1. Symbols and Units 213 Appendix 2. Tables and Diagrams of Natural Values 219 Appendix 3. Symbols and Basic Conversion Factors 237 Appendix 4. International Standard Atmosphere, SI Units 239 Appendix 5. International Standard Atmosphere, in BS 251 Appendix 6. NACA Airfoils’ Diagrams 259 Bibliography 287 Index 289

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Book Synopsis Mechanical behaviors of materials are highly influenced by their architectures and/or microstructures. Hence, progress in material science involves understanding and modeling the link between the microstructure and the material behavior at different scales. This book gathers contributions from eminent researchers in the field of computational and experimental material modeling. It presents advanced experimental techniques to acquire the microstructure features together with dedicated numerical and analytical tools to take into account the randomness of the micro-structure. Table of ContentsPreface xi Chapter 1. Synchrotron Imaging and Diffraction for In Situ 3D Characterization of Polycrystalline Materials 1Henry PROUDHON 1.1. Introduction 1 1.2. 3D X-ray characterization of structural materials 3 1.2.1. Early days of X-ray computed tomography 3 1.2.2. X-ray absorption and Beer Lambert’s law 4 1.2.3. X-ray detection 6 1.2.4. Radon’s transform and reconstruction 8 1.2.5. Synchrotron X-ray microtomography 10 1.2.6. Phase contrast tomography 13 1.2.7. Diffraction contrast tomography 14 1.3. Nanox: a miniature mechanical stress rig designed for near-field X-ray diffraction imaging techniques 16 1.4. Coupling diffraction contrast tomography with the finite-element method. 19 1.4.1. Motivation for image-based mechanical computations 19 1.4.2. 3D mesh generation from tomographic images 20 1.4.3. Toward a fatigue model at the scale of the polycrystal 28 1.5. Conclusion and outlook 29 1.6. Bibliography 31 Chapter 2. Determining the Probability of Occurrence of Rarely Occurring Microstructural Configurations for Titanium Dwell Fatigue 41Adam L. PILCHAK, Joseph C. TUCKER and Tyler J. WEIHING 2.1. Introduction 42 2.2. Experimental methods 44 2.2.1. MTR quantification metrics 44 2.2.2. Synthetic microstructure generation 46 2.2.3. Crystallographic analysis for titanium dwell fatigue 48 2.2.4. Block maxima 50 2.3. Results and discussion 51 2.3.1. Probability of occurrence 53 2.3.2. “Hard” MTR size distributions 57 2.3.3. Block maxima 58 2.4. Summary and outlook 63 2.5. Bibliography 64 Chapter 3. Wave Propagation Analysis in 2D Nonlinear Periodic Structures Prone to Mechanical Instabilities 67Hilal REDA, Yosra RAHALI, Jean-François GANGHOFFER and Hassan LAKISS 3.1. Introduction 68 3.2. Extensible energy of pantograph for dynamic analysis 70 3.2.1. Expression of the pantographic network energy 70 3.2.2. Dynamic equilibrium equation 73 3.3. Wave propagation in a nonlinear elastic beam 75 3.3.1. Legendre–Hadamard ellipticity condition and loss of stability 77 3.3.2. Supersonic and subsonic modes for 1D wave propagation 78 3.3.3. Wave dispersion relation in 2D nonlinear periodic structures 81 3.3.4. Anisotropic behavior of 2D pantographic networks versus the degree of nonlinearity 84 3.4. Conclusion 85 3.5. Appendix 86 3.6. Bibliography 94 Chapter 4. Multiscale Model of Concrete Failure 99Emir KARAVELIĆ, Mijo NIKOLIĆ and Adnan IBRAHIMBEGOVIĆ 4.1. Introduction 99 4.2. Meso-scale model 102 4.3. Macroscopic model response 106 4.3.1. Uniaxial tests 106 4.3.2. Failure surface 111 4.4. Conclusions 117 4.5. Acknowledgments 119 4.6. Bibliography 120 Chapter 5. Discrete Numerical Simulations of the Strength and Microstructure Evolution During Compaction of Layered Granular Solids 123Bereket YOHANNES, Marcial GONZALEZ and Alberto M. CUITIÑO 5.1. Introduction 123 5.2. Numerical simulation 127 5.2.1. Discrete particle simulations of powder compaction 127 5.2.2. Discrete particle simulation of layered compacts 129 5.3. Discussion 131 5.4. Conclusion 137 5.5. Acknowledgements 137 5.6. Bibliography 137 Chapter 6. Microstructural Views of Stresses in Three-Phase Granular Materials 143Jérôme DURIEZ, Richard WAN and Félix DARVE 6.1. Microstructural expression of triphasic total stresses 145 6.1.1. Stress description within micro-scale volumes and interfaces of triphasic materials 145 6.1.2. Total stress derivation 146 6.2. Numerical modeling of wet ideal granular materials 149 6.2.1. DEM description of fluid microstructure 149 6.2.2. DEM description of stress and strains 152 6.3. Anisotropy of the capillary stress contribution 154 6.3.1. Mechanical loading 155 6.3.2. Hydraulic loading 157 6.4. Effective stress 160 6.5. Conclusion 162 6.6. Bibliography 163 Chapter 7. Effect of the Third Invariant of the Stress Deviator on the Response of Porous Solids with Pressure-Insensitive Matrix 167José Luis ALVES and Oana CAZACU 7.1. Introduction 168 7.2. Problem statement and method of analysis 171 7.2.1. Drucker yield criterion for isotropic materials 171 7.2.2. Unit cell model 173 7.3. Results 179 7.3.1. Yield surfaces and porosity evolution 179 7.4. Conclusions 190 7.5. Bibliography 194 Chapter 8. High Performance Data-Driven Multiscale Inverse Constitutive Characterization of Composites 197John MICHOPOULOS, Athanasios ILIOPOULOS, John HERMANSON, John STEUBEN and Foteini KOMNINELI 8.1. Introduction 198 8.2. Automated multi-axial testing 202 8.2.1. Loading space 204 8.2.2. Experimental campaign 206 8.3. Constitutive formalisms 207 8.3.1. Small strain formulation 208 8.3.2. Finite strain formulation 209 8.4. Meshless random grid method for experimental evaluation of strain fields 209 8.5. Inverse determination of HDM via design optimization 211 8.5.1. Numerical results of design optimization 214 8.6. Surrogate models for characterization 216 8.6.1. Definition and construction of the surrogate model 218 8.6.2. Characterization by optimization 219 8.6.3. Validation with physical experiments 221 8.7. Multi-scale inversion 221 8.7.1. Forward problem: mathematical homogenization 222 8.7.2. Inverse problem 224 8.8. Computational framework and synthetic experiments 226 8.9. Conclusions and plans 230 8.10. Acknowledgments 232 8.11. Bibliography 232 Chapter 9. New Trends in Computational Mechanics: Model Order Reduction, Manifold Learning and Data-Driven 239Jose Vicente AGUADO, Domenico BORZACCHIELLO, Elena LOPEZ, Emmanuelle ABISSET-CHAVANNE, David GONZALEZ, Elias CUETO and Francisco CHINESTA 9.1. Introduction 240 9.1.1. The big picture 240 9.1.2. The PGD at a glance 242 9.2. Constructing slow manifolds 245 9.2.1. From principal component analysis (PCA) to kernel principal component analysis (kPCA) 245 9.2.2. Kernel principal component analysis (kPCA) 249 9.2.3. Locally linear embedding (LLE) 250 9.2.4. Discussion 251 9.3. Manifold-learning-based computational mechanics 252 9.4. Data-driven simulations 253 9.4.1. Data-based weak form 254 9.4.2. Constructing the constitutive manifold 254 9.5. Data-driven upscaling of viscous flows in porous media 257 9.5.1. Upscaling Newtonian and generalized Newtonian fluids flowing in porous media 258 9.6. Conclusions 260 9.7. Bibliography 261 List of Authors 267 Index 271

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Book SynopsisThis book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the Helmholtz-Hodge decomposition plays an important role.Trade Review"This book develops a new and original approach to mechanics." (Zentralblatt MATH, 1 June 2015)Table of ContentsPREFACE ix LIST OF SYMBOLS xv INTRODUCTION xxi CHAPTER 1. FRAMEWORK OF DISCRETE MECHANICS 1 1.1. Frames of reference and uniform motions 1 1.2. Concept of a Discrete Medium 4 1.2.1. Vectors and components 6 1.2.2. Physical meaning of the differential operators 8 1.2.3. Use of the theorems of differential geometry 10 1.2.4. Two essential properties 12 1.2.5. Tensorial values 17 1.2.6. The scalar and vectorial potentials 19 1.3. The physical characteristics 20 1.4. Equilibrium stress state 22 1.4.1. Two examples of mechanical equilibrium 25 1.5. Thermodynamic non-equilibrium 26 1.5.1. Forces and fluxes 29 1.6. Conservation of mass 30 CHAPTER 2. MOMENTUM CONSERVATION 33 2.1. Classification of forces 33 2.2. Three fundamental experiments 35 2.2.1. Equilibrium in a glass of water 35 2.2.2. Couette flow 44 2.2.3. Poiseuille flow 47 2.3. Postulates 51 2.4. Modeling of the pressure forces 52 2.5. Modeling of the viscous forces 57 2.5.1. Modeling of the viscous effects of volume 57 2.5.2. Modeling of the viscous surface effects 59 2.5.3. Stress state 62 2.6. Objectivity 64 2.7. Discrete motion balance equation 67 2.7.1. Fundamental law of dynamics 67 2.7.2. Eulerian step 73 2.7.3. Mechanical equilibrium 74 2.8. Formulation in terms of density and temperature 78 2.9. Similitude parameters 81 2.9.1. Impact on the surface of a liquid 85 2.10. Hypercompressible media 88 CHAPTER 3. CONSERVATION OF HEAT FLUX AND ENERGY 91 3.1. Introduction 91 3.2. Conservation of flux 92 3.3. Conservation of energy 95 3.3.1. Conservation of total energy 95 3.3.2. Conservation of kinetic energy 97 3.3.3. Conservation of the internal energy 98 3.4. Discrete equations for the flux and the energy 99 3.5. A simple heat-conduction problem 100 3.5.1. Case of anisotropic materials 102 CHAPTER 4. PROPERTIES OF DISCRETE EQUATIONS 105 4.1. A system of equations and potentials 105 4.2. Physics represented 107 4.2.1. Poiseuille flow and potentials 110 4.2.2. Celerity and maximum velocity 112 4.2.3. Remarks about turbulence 113 4.3. Boundary conditions 114 4.3.1. Contact surface 114 4.3.2. Shockwaves 117 4.3.3. Edge conditions 118 4.3.4. Slip condition 119 4.3.5. Capillary effects 120 4.3.6. Thermal boundary conditions 124 4.4. Penalization of the potentials 125 4.5. Continua and discrete mediums 129 4.5.1. Differences with the Navier–Stokes equation 129 4.5.2. Dissipation 133 4.5.3. Case of rigidifying motions 135 4.5.4. An example of the dissipation of energy 137 4.6. Hodge–Helmholtz decomposition 139 4.7. Approximations 141 4.7.1. Bernoulli’s law 141 4.7.2. Irrotational flow 143 4.7.3. Inviscid fluid 144 4.7.4. Incompressible flow 145 4.8. Gravitational waves 147 4.9. Linear visco-elasticity 150 4.9.1. Viscous dissipation in a visco-elastic medium 153 4.9.2. Dissipation of longitudinal waves in a visco-elastic medium 155 4.9.3. Consistency with Continuum Mechanics 156 4.9.4. Pure compression 159 4.9.5. Pure shear stress 160 4.9.6. Bingham fluid 162 CHAPTER 5. MULTIPHYSICS 165 5.1. Extensions to other branches of physics 165 5.1.1. Coupling between a fluid and a porous medium 167 5.2. Flow around a cylinder in an infinite medium 169 5.2.1. Darcian model 170 5.2.2. Stokes model 174 5.2.3. Model of an ideal fluid 175 5.2.4. Brinkman model 176 5.3. Fluid statics 178 5.3.1. Perfect gas in isothermal evolution 179 5.3.2. Perfect gas in adiabatic evolution 181 5.4. Injection of a gas into a cavity 183 5.4.1. Isothermal injection 184 5.4.2. Adiabatic injection 185 5.5. Nonlinear wave propagation 188 5.5.1. Sod shock tube 190 5.6. Thermo-acoustics 192 5.6.1. Heating of a cavity filled with air 193 5.7. Natural convection in an enclosed cavity 198 5.8. Multi-component transport 200 5.9. Modeling of phase change 203 5.10. Critical opalescence 207 5.11. Conclusions regarding the multiphysics approach 209 APPENDIX 211 BIBLIOGRAPHY 215 INDEX 219

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Book SynopsisThe Fifth edition of this classic textbook includes a solutions manual. Extensive supplemental instructor resources are forthcoming in the Fall of 2022.Mechanical Vibration: Theory and Application presents comprehensive coverage of the fundamental principles of mechanical vibration, including the theory of vibration, as well as discussions and examples of the applications of these principles to practical engineering problems. The book also addresses the effects of uncertainties in vibration analysis and design and develops passive and active methods for the control of vibration. Many example problems with solutions are provided. These examples as well as compelling case studies and stories of real-world applications of mechanical vibration have been carefully chosen and presented to help the reader gain a thorough understanding of the subject. There is a solutions manual for instructors who adopt this book. Request a solutions manual here (https://www.rutgersuniversitypress.org/mechanical-vibration).Trade ReviewThis fifth edition of Mechanical Vibration, a broad and deep exposition not only of vibration, but also of system uncertainties and control, has been expanded and re-written in many parts. The comprehensive coverage includes elementary as well as advanced and professional topics. There are numerous engineering case studies, new appendixes on damping models, and extensive MATLAB resources. The exposition of concepts is careful and precise and yet the presentation is casual, a combination that makes the book remarkably easy and enjoyable to read. -- Fai Ma * Mechanical Engineering, University of California, Berkeley *Mechanical vibration permeates every aspect of engineering design including automotive, aerospace, electronics, machine tools, robotics and structural systems. This text provides a well-integrated, clear and concise discussion of the theory and practice of mechanical vibration as well as the related subjects of random vibration and vibration control. It presents a wide array of real-world examples and meaningful case studies, highlighted by interesting photographs that motivate the subject. There are many solved problems, detailed derivations, and insights that draw on the academic and industrial experiences of the authors. Some of the examples address very classical systems, and others target next generation systems that are currently at the leading edge of technology. The authors are to be congratulated for writing an engaging textbook that makes the challenging and important subject of vibration accessible to engineering students in various disciplines. -- Thomas R. Kurfess * George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology *For a broad range of engineers involved in structural analysis, this is, in my opinion, a definitely "must have" book. It is perfectly relevant to numerous applications of vibrational analysis in civil, mechanical, aerospace, and biomechanical engineering fields. Although it is written primarily as a textbook, an experienced reader will find it equally useful as a systematic reference of major modern concepts, solutions, and demonstrations cases. The authors have found an optimum balance between “mathematical” and “applied” sides, emphasizing, on one hand, the motivation and modeling of reality, and lessons learned from generated results and, on the other hand, providing rigorous mathematical implementations in a very clear and logical way. The book is extremely well written, and very easy to read, with numerous examples. It also includes an appendix with extensive MATLAB programs for quick implementation into engineering practice. I especially value the chapters on random vibration that demonstrate the importance of probabilistic solutions of structural reliability. It is also a pleasure indeed to read historical anecdotes and life sketches and understand the development of modern mechanics as a process. -- Mark Gurvich * Technical Fellow, Collins Aerospace *Whether tuning a suspension, maximizing tire grip, honing a cylinder bore or determining (just enough) engine isolation, the topic of vibration is critical to vehicle design. This book is impressive, not only in its scope, but also in its approach. The presentation of material is well thought-out, the examples and derivations are quite detailed and easy to follow, while the prose, pictures and bios provide unique context that make the subject matter surprisingly engaging. Aside from making this broad topic approachable to students, this book serves as a concise reference for professionals. The inclusion of an overview of basic (time domain) controls, as well as random vibration, adds additional value and perspective. -- Jim Sadauckas * Staff System Engineer, Vehicle Dynamics & Simulation, Harley-Davidson Motor Company *In the design of vehicles, vibration is a constant issue as it influences complete vehicle properties such as cabin comfort, driving performance, and vehicle dynamics and can lead to fatigue, damage, and failure. Control of vibration is a key factor in successful vehicle design, making this book on modern vibration highly relevant. The book connects theory with practice, includes many worked examples and case studies, and is a resource on vibration that imparts deep physical as well as mathematical understanding to the student or engineer. It is highly recommended. -- Julian Weber * Head of Innovation Projects E-Mobility, BMW *I have heard people say that good writing has a ‘voice.’ Mechanical Vibration by Benaroya, Nagurka, and Han has a voice that tells a rich story about vibration analysis in all its glory – from the beauty of its mathematics through its impact on our daily lives to the history of the people who brought it to life. -- Keith Buffinton * Dean of Engineering, emeritus, Bucknell University *Table of Contents1. INTRODUCTION AND BACKGROUND2. SINGLE DEGREE-OF-FREEDOM UNDAMPED VIBRATION 3. SINGLE DEGREE-OF-FREEDOM DAMPED VIBRATION4. SINGLE DOF VIBRATION: GENERAL LOADING AND ADVANCED TOPICS5. VARIATIONAL PRINCIPLES AND ANALYTICAL DYNAMICS6. MULTI DEGREE-OF-FREEDOM VIBRATION7. CONTINUOUS MODELS FOR VIBRATION 8. CONTINUOUS MODELS FOR VIBRATION: ADVANCED MODELS9. RANDOM VIBRATION: PROBABILISTIC FORCES10. VIBRATION CONTROL 11. NONLINEAR VIBRATIONA: MATHEMATICAL CONCEPTS FOR VIBRATIONB: VISCOELASTIC DAMPINGC: SOLVING VIBRATION PROBLEMS WITH MATLABIndex

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