{"product_id":"formulas-for-dynamics-acoustics-and-vibration-9781119038115","title":"Formulas for Dynamics Acoustics and Vibration","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWith Over 60 tables, most with graphic illustration, and over 1000 formulas, Formulas for Dynamics, Acoustics, and Vibration will provide an invaluable time-saving source of concise solutions for mechanical, civil, nuclear, petrochemical and aerospace engineers and designers.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Definitions, Units, and Geometric Properties 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Definitions 1\u003c\/p\u003e \u003cp\u003e1.2 Symbols 8\u003c\/p\u003e \u003cp\u003e1.3 Units 11\u003c\/p\u003e \u003cp\u003e1.4 Motion on the Surface of the Earth 18\u003c\/p\u003e \u003cp\u003e1.5 Geometric Properties of Plane Areas 19\u003c\/p\u003e \u003cp\u003e1.6 Geometric Properties of Rigid Bodies 30\u003c\/p\u003e \u003cp\u003e1.7 Geometric Properties Defined by Vectors 40\u003c\/p\u003e \u003cp\u003eReferences 41\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Dynamics of Particles and Bodies 43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Kinematics and Coordinate Transformations 43\u003c\/p\u003e \u003cp\u003e2.2 Newton’s Law of Particle Dynamics 50\u003c\/p\u003e \u003cp\u003e2.2.1 Constant Mass Systems 50\u003c\/p\u003e \u003cp\u003e2.2.2 Variable Mass Systems 57\u003c\/p\u003e \u003cp\u003e2.2.3 Particle Trajectories 58\u003c\/p\u003e \u003cp\u003e2.2.4 Work and Energy 63\u003c\/p\u003e \u003cp\u003e2.2.5 Impulse 65\u003c\/p\u003e \u003cp\u003e2.2.6 Armor 68\u003c\/p\u003e \u003cp\u003e2.2.7 Gravitation and Orbits 71\u003c\/p\u003e \u003cp\u003e2.3 Rigid Body Rotation 73\u003c\/p\u003e \u003cp\u003e2.3.1 Rigid Body Rotation Theory 73\u003c\/p\u003e \u003cp\u003e2.3.2 Single-Axis Rotation 73\u003c\/p\u003e \u003cp\u003e2.3.3 Multiple-Axis Rotation 84\u003c\/p\u003e \u003cp\u003e2.3.4 Gyroscopic Effects 85\u003c\/p\u003e \u003cp\u003eReferences 87\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Natural Frequency of Spring–Mass Systems, Pendulums, Strings, and Membranes 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Harmonic Motion 89\u003c\/p\u003e \u003cp\u003e3.2 Spring Constants 91\u003c\/p\u003e \u003cp\u003e3.3 Natural Frequencies of Spring–Mass Systems 99\u003c\/p\u003e \u003cp\u003e3.3.1 Single-Degree-of-Freedom 99\u003c\/p\u003e \u003cp\u003e3.3.2 Two-Degree-of-Freedom System 113\u003c\/p\u003e \u003cp\u003e3.4 Modeling Discrete Systems with Springs and Masses 117\u003c\/p\u003e \u003cp\u003e3.4.1 Springs with Mass 117\u003c\/p\u003e \u003cp\u003e3.4.2 Bellows 118\u003c\/p\u003e \u003cp\u003e3.5 Pendulum Natural Frequencies 119\u003c\/p\u003e \u003cp\u003e3.5.1 Mass Properties from Frequency Measurement 120\u003c\/p\u003e \u003cp\u003e3.6 Tensioned Strings, Cables, and Chain Natural Frequencies 121\u003c\/p\u003e \u003cp\u003e3.6.1 Equation of Motion 121\u003c\/p\u003e \u003cp\u003e3.6.2 Cable Sag 123\u003c\/p\u003e \u003cp\u003e3.7 Membrane Natural Frequencies 126\u003c\/p\u003e \u003cp\u003e3.7.1 Flat Membranes 126\u003c\/p\u003e \u003cp\u003e3.7.2 Curved Membranes 131\u003c\/p\u003e \u003cp\u003eReferences 132\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Natural Frequency of Beams 134\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Beam Bending Theory 134\u003c\/p\u003e \u003cp\u003e4.1.1 Stress, Strain, and Deformation 134\u003c\/p\u003e \u003cp\u003e4.1.2 Sandwich Beams 136\u003c\/p\u003e \u003cp\u003e4.1.3 Beam Equation of Motion 137\u003c\/p\u003e \u003cp\u003e4.1.4 Boundary Conditions and Modal Solution 137\u003c\/p\u003e \u003cp\u003e4.1.5 Beams on Elastic Foundations 141\u003c\/p\u003e \u003cp\u003e4.1.6 Simplification for Tubes 141\u003c\/p\u003e \u003cp\u003e4.2 Natural Frequencies and Mode Shapes of Single-Span and Multiple-Span Beams 142\u003c\/p\u003e \u003cp\u003e4.2.1 Single-Span Beams 142\u003c\/p\u003e \u003cp\u003e4.2.2 Orthogonality, Normalization, and Maximum Values 150\u003c\/p\u003e \u003cp\u003e4.2.3 Beams Stress 150\u003c\/p\u003e \u003cp\u003e4.2.4 Two-Span Beams 151\u003c\/p\u003e \u003cp\u003e4.2.5 Multispan Beams 151\u003c\/p\u003e \u003cp\u003e4.3 Axially Loaded Beam Natural Frequency 158\u003c\/p\u003e \u003cp\u003e4.3.1 Uniform Axial Load 158\u003c\/p\u003e \u003cp\u003e4.3.2 Linearly Varying Axial Load 159\u003c\/p\u003e \u003cp\u003e4.4 Beams with Masses, Tapered Beams, Beams with Spring Supports, and Shear Beams 162\u003c\/p\u003e \u003cp\u003e4.4.1 Beams with Masses 162\u003c\/p\u003e \u003cp\u003e4.4.2 Tapered and Stepped Beams 162\u003c\/p\u003e \u003cp\u003e4.4.3 Spring-Supported Beams 167\u003c\/p\u003e \u003cp\u003e4.4.4 Shear Beams 167\u003c\/p\u003e \u003cp\u003e4.4.5 Effect of Shearing Force on the Deflections of Beams 170\u003c\/p\u003e \u003cp\u003e4.4.6 Rotary Inertia 170\u003c\/p\u003e \u003cp\u003e4.4.7 Multistory Buildings 174\u003c\/p\u003e \u003cp\u003e4.5 Torsional and Longitudinal Beam Natural Frequencies 176\u003c\/p\u003e \u003cp\u003e4.5.1 Longitudinal Vibration of Beams and Springs 176\u003c\/p\u003e \u003cp\u003e4.5.2 Torsional Vibration of Beams and Shafts 179\u003c\/p\u003e \u003cp\u003e4.5.3 Circular Cross Section 179\u003c\/p\u003e \u003cp\u003e4.5.4 Noncircular Cross Sections 182\u003c\/p\u003e \u003cp\u003e4.6 Wave Propagation in Beams 183\u003c\/p\u003e \u003cp\u003e4.7 Curved Beams, Rings, and Frames 184\u003c\/p\u003e \u003cp\u003e4.7.1 Complete Rings 184\u003c\/p\u003e \u003cp\u003e4.7.2 Stress and Strain of Arcs 189\u003c\/p\u003e \u003cp\u003e4.7.3 Supported Rings and Helices 190\u003c\/p\u003e \u003cp\u003e4.7.4 Circular Arcs, Arches, and Bends 190\u003c\/p\u003e \u003cp\u003e4.7.5 Lowest Frequency In-Plane Natural Frequency of an Arc 196\u003c\/p\u003e \u003cp\u003e4.7.6 Shallow Arc 197\u003c\/p\u003e \u003cp\u003e4.7.7 Portal Frames 198\u003c\/p\u003e \u003cp\u003eReferences 199\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Natural Frequency of Plates and Shells 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Plate Flexure Theory 203\u003c\/p\u003e \u003cp\u003e5.1.1 Stress and Strain 203\u003c\/p\u003e \u003cp\u003e5.1.2 Boundary Conditions 203\u003c\/p\u003e \u003cp\u003e5.1.3 Plate Equation of Motion 205\u003c\/p\u003e \u003cp\u003e5.1.4 Simply Supported Rectangular Plate 206\u003c\/p\u003e \u003cp\u003e5.1.5 Plates on Elastic Foundations 207\u003c\/p\u003e \u003cp\u003e5.1.6 Sandwich Plates 207\u003c\/p\u003e \u003cp\u003e5.1.7 Thick Plates and Shear Deformation 207\u003c\/p\u003e \u003cp\u003e5.1.8 Membrane Analogy and In-Plane Loads 208\u003c\/p\u003e \u003cp\u003e5.1.9 Orthogonality 208\u003c\/p\u003e \u003cp\u003e5.2 Plate Natural Frequencies and Mode Shapes 209\u003c\/p\u003e \u003cp\u003e5.2.1 Plate Natural Frequencies 209\u003c\/p\u003e \u003cp\u003e5.2.2 Circular and Annular Plates 209\u003c\/p\u003e \u003cp\u003e5.2.3 Sectorial and Circular Orthotropic Plates 214\u003c\/p\u003e \u003cp\u003e5.2.4 Rectangular Plates 214\u003c\/p\u003e \u003cp\u003e5.2.5 Parallelogram, Triangular and Point-Supported Plates 215\u003c\/p\u003e \u003cp\u003e5.2.6 Rectangular Orthotropic Plates and Grillages 215\u003c\/p\u003e \u003cp\u003e5.2.7 Stiffened Plates 231\u003c\/p\u003e \u003cp\u003e5.2.8 Perforated Plates 232\u003c\/p\u003e \u003cp\u003e5.3 Cylindrical Shells 234\u003c\/p\u003e \u003cp\u003e5.3.1 Donnell Thin Shell Theory 235\u003c\/p\u003e \u003cp\u003e5.3.2 Natural Frequencies of Cylindrical Shells 237\u003c\/p\u003e \u003cp\u003e5.3.3 Infinitely Long Cylindrical Shell Modes (j=0) 241\u003c\/p\u003e \u003cp\u003e5.3.4 Simply Supported Cylindrical Shells without Axial Constraint 243\u003c\/p\u003e \u003cp\u003e5.3.5 Cylindrical Shells with Other Boundary Conditions 246\u003c\/p\u003e \u003cp\u003e5.3.6 Free–Free Cylindrical Shell 248\u003c\/p\u003e \u003cp\u003e5.3.7 Cylindrically Curved Panels 249\u003c\/p\u003e \u003cp\u003e5.3.8 Effect of Mean Load on Natural Frequencies 250\u003c\/p\u003e \u003cp\u003e5.4 Spherical and Conical Shells 250\u003c\/p\u003e \u003cp\u003e5.4.1 Spherical Shells 250\u003c\/p\u003e \u003cp\u003e5.4.2 Open Shells and Church Bells 252\u003c\/p\u003e \u003cp\u003e5.4.3 Shallow Spherical Shells 252\u003c\/p\u003e \u003cp\u003e5.4.4 Conical Shells 254\u003c\/p\u003e \u003cp\u003eReferences 254\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Acoustics and Fluids 260\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Sound Waves and Decibels 260\u003c\/p\u003e \u003cp\u003e6.1.1 Speed of Sound 260\u003c\/p\u003e \u003cp\u003e6.1.2 Acoustic Wave Equation 264\u003c\/p\u003e \u003cp\u003e6.1.3 Decibels and Sound Power Level 276\u003c\/p\u003e \u003cp\u003e6.1.4 Standards for Measurement 277\u003c\/p\u003e \u003cp\u003e6.1.5 Attenuation and Transmission Loss (TL) 278\u003c\/p\u003e \u003cp\u003e6.2 Sound Propagation in Large Spaces 285\u003c\/p\u003e \u003cp\u003e6.2.1 Acoustic Wave Propagation 285\u003c\/p\u003e \u003cp\u003e6.2.2 Sound Pressure on Rigid Walls 288\u003c\/p\u003e \u003cp\u003e6.2.3 Mass Law for Sound Transmission 289\u003c\/p\u003e \u003cp\u003e6.3 Acoustic Waves in Ducts and Rooms 289\u003c\/p\u003e \u003cp\u003e6.3.1 Acoustic Waves in Ducts 289\u003c\/p\u003e \u003cp\u003e6.3.2 Mufflers and Resonators 298\u003c\/p\u003e \u003cp\u003e6.3.3 Room Acoustics 302\u003c\/p\u003e \u003cp\u003e6.4 Acoustic Natural Frequencies and Mode Shapes 305\u003c\/p\u003e \u003cp\u003e6.4.1 Structure-Acoustic Analogy 306\u003c\/p\u003e \u003cp\u003e6.5 Free Surface Waves and Liquid Sloshing 310\u003c\/p\u003e \u003cp\u003e6.6 Ships and Floating Systems 319\u003c\/p\u003e \u003cp\u003e6.6.1 Ship Natural Frequencies (1\/Period) 319\u003c\/p\u003e \u003cp\u003e6.7 Added Mass of Structure in Fluids 321\u003c\/p\u003e \u003cp\u003e6.7.1 Added Mass Potential Flow Theory 328\u003c\/p\u003e \u003cp\u003e6.7.2 Added Mass 329\u003c\/p\u003e \u003cp\u003e6.7.3 Added Mass of Plates and Shells 330\u003c\/p\u003e \u003cp\u003eReferences 331\u003c\/p\u003e \u003cp\u003eFurther Reading 335\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Forced Vibration 336\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Steady-State Forced Vibration 336\u003c\/p\u003e \u003cp\u003e7.1.1 Single-Degree-of-Freedom Spring–Mass Response 336\u003c\/p\u003e \u003cp\u003e7.1.2 Multiple-Degree-of-Freedom Spring–Mass System Response 344\u003c\/p\u003e \u003cp\u003e7.1.3 Forced Harmonic Vibration of Continuous Systems 347\u003c\/p\u003e \u003cp\u003e7.1.4 General System Response 357\u003c\/p\u003e \u003cp\u003e7.2 Transient Vibration 359\u003c\/p\u003e \u003cp\u003e7.2.1 Transient Vibration Theory 359\u003c\/p\u003e \u003cp\u003e7.2.2 Continuous Systems and Initial Conditions 365\u003c\/p\u003e \u003cp\u003e7.2.3 Maximum Transient Response and Response Spectra 371\u003c\/p\u003e \u003cp\u003e7.2.4 Shock Standards and Shock Test Machines 374\u003c\/p\u003e \u003cp\u003e7.3 Vibration Isolation 374\u003c\/p\u003e \u003cp\u003e7.3.1 Single-Degree-of-Freedom Vibration Isolation 374\u003c\/p\u003e \u003cp\u003e7.3.2 Two-Degree-of-Freedom Vibration Isolation 377\u003c\/p\u003e \u003cp\u003e7.4 Random Vibration Response to Spectral Loads 379\u003c\/p\u003e \u003cp\u003e7.4.1 Power Spectral Density and Fourier Series 380\u003c\/p\u003e \u003cp\u003e7.4.2 Complex Fourier Transform and Random Response 381\u003c\/p\u003e \u003cp\u003e7.5 Approximate Response Solution 385\u003c\/p\u003e \u003cp\u003e7.5.1 Equivalent Static Loads 389\u003c\/p\u003e \u003cp\u003e7.5.2 Scaling Mode Shapes to Load 389\u003c\/p\u003e \u003cp\u003eReferences 391\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Properties of Solids, Liquids, and Gases 392\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Solids 392\u003c\/p\u003e \u003cp\u003e8.2 Liquids 402\u003c\/p\u003e \u003cp\u003e8.3 Gases 405\u003c\/p\u003e \u003cp\u003e8.3.1 Ideal Gas Law 405\u003c\/p\u003e \u003cp\u003eReferences 409\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Approximate Methods for Natural Frequency 410\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Relationship between Fundamental Natural Frequency and Static Deflection 410\u003c\/p\u003e \u003cp\u003eA.2 Rayleigh Technique 413\u003c\/p\u003e \u003cp\u003eA.3 Dunkerley and Southwell Methods 415\u003c\/p\u003e \u003cp\u003eA.4 Rayleigh–Ritz and Schmidt Approximations 415\u003c\/p\u003e \u003cp\u003eA.5 Galerkin Procedure for Continuous Structures 416\u003c\/p\u003e \u003cp\u003eReferences 417\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Numerical Integration of Newton’s Second Law 418\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences 421\u003c\/p\u003e \u003cp\u003e\u003cb\u003eC Standard Octaves and Sound Pressure 422\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 Time History and Overall Sound Pressure 422\u003c\/p\u003e \u003cp\u003eC.2 Peaks and Crest 423\u003c\/p\u003e \u003cp\u003eC.3 Spectra and Spectral Density 424\u003c\/p\u003e \u003cp\u003eC.4 Logarithmic Frequency Scales and Musical Tunings 424\u003c\/p\u003e \u003cp\u003eC.5 Human Perception of Sound (Psychological Acoustics) 426\u003c\/p\u003e \u003cp\u003eReferences 427\u003c\/p\u003e \u003cp\u003e\u003cb\u003eD Integrals Containing Mode Shapes of Single-Span Beams 429\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReference 429\u003c\/p\u003e \u003cp\u003e\u003cb\u003eE Finite Element Programs 435\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eE.1 Professional\/Commercial Programs 435\u003c\/p\u003e \u003cp\u003eE.2 Open Source \/Low-Cost Programs 436\u003c\/p\u003e \u003cp\u003eIndex 439\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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