{"product_id":"asymptotic-methods-in-the-theory-of-plates-with-mixed-boundary-conditions-9781118725191","title":"Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAsymptotic Methods in the Theory of Plates with Mixed Boundary Conditions comprehensively covers the theoretical background of asymptotic approaches and their use in solving mechanical engineering-oriented problems of structural members, primarily plates (statics and dynamics)  with mixed boundary conditions.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003eList of Abbreviations xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Asymptotic Approaches 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1.1 Asymptotic Series and Approximations 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1.1 Asymptotic Series 1\u003c\/p\u003e \u003cp\u003e1.1.2 Asymptotic Symbols and Nomenclatures 5\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1.2 Some Nonstandard Perturbation Procedures 8\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.2.1 Choice of Small Parameters 8\u003c\/p\u003e \u003cp\u003e1.2.2 Homotopy Perturbation Method 10\u003c\/p\u003e \u003cp\u003e1.2.3 Method of Small Delta 13\u003c\/p\u003e \u003cp\u003e1.2.4 Method of Large Delta 17\u003c\/p\u003e \u003cp\u003e1.2.5 Application of Distributions 19\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1.3 Summation of Asymptotic Series 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.3.1 Analysis of Power Series 21\u003c\/p\u003e \u003cp\u003e1.3.2 Padé Approximants and Continued Fractions 24\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1.4 Some Applications of PA 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.4.1 Accelerating Convergence of Iterative Processes 29\u003c\/p\u003e \u003cp\u003e1.4.2 Removing Singularities and Reducing the Gibbs-Wilbraham Effect 31\u003c\/p\u003e \u003cp\u003e1.4.3 Localized Solutions 32\u003c\/p\u003e \u003cp\u003e1.4.4 Hermite-Padé Approximations and Bifurcation Problem 34\u003c\/p\u003e \u003cp\u003e1.4.5 Estimates of Effective Characteristics of Composite Materials 34\u003c\/p\u003e \u003cp\u003e1.4.6 Continualization 35\u003c\/p\u003e \u003cp\u003e1.4.7 Rational Interpolation 36\u003c\/p\u003e \u003cp\u003e1.4.8 Some Other Applications 37\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1.5 Matching of Limiting Asymptotic Expansions 38\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.5.1 Method of Asymptotically Equivalent Functions for Inversion of Laplace Transform 38\u003c\/p\u003e \u003cp\u003e1.5.2 Two-Point PA 41\u003c\/p\u003e \u003cp\u003e1.5.3 Other Methods of AEFs Construction 43\u003c\/p\u003e \u003cp\u003e1.5.4 Example: Schrödinger Equation 45\u003c\/p\u003e \u003cp\u003e1.5.5 Example: AEFs in the Theory of Composites 46\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1.6 Dynamical Edge Effect Method 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.6.1 Linear Vibrations of a Rod 49\u003c\/p\u003e \u003cp\u003e1.6.2 Nonlinear Vibrations of a Rod 51\u003c\/p\u003e \u003cp\u003e1.6.3 Nonlinear Vibrations of a Rectangular Plate 54\u003c\/p\u003e \u003cp\u003e1.6.4 Matching of Asymptotic and Variational Approaches 58\u003c\/p\u003e \u003cp\u003e1.6.5 On the Normal Forms of Nonlinear Vibrations of Continuous Systems 60\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1.7 Continualization 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.7.1 Discrete and Continuum Models in Mechanics 61\u003c\/p\u003e \u003cp\u003e1.7.2 Chain of Elastically Coupled Masses 62\u003c\/p\u003e \u003cp\u003e1.7.3 Classical Continuum Approximation 64\u003c\/p\u003e \u003cp\u003e1.7.4 \"Splashes\" 65\u003c\/p\u003e \u003cp\u003e1.7.5 Envelope Continualization 66\u003c\/p\u003e \u003cp\u003e1.7.6 Improvement Continuum Approximations 68\u003c\/p\u003e \u003cp\u003e1.7.7 Forced Oscillations 69\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1.8 Averaging and Homogenization 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.8.1 Averaging via Multiscale Method 71\u003c\/p\u003e \u003cp\u003e1.8.2 Frozing in Viscoelastic Problems 74\u003c\/p\u003e \u003cp\u003e1.8.3 The WKB Method 75\u003c\/p\u003e \u003cp\u003e1.8.4 Method of Kuzmak-Whitham (Nonlinear WKB Method) 77\u003c\/p\u003e \u003cp\u003e1.8.5 Differential Equations with Quickly Changing Coefficients 79\u003c\/p\u003e \u003cp\u003e1.8.6 Differential Equation with Periodically Discontinuous Coefficients 84\u003c\/p\u003e \u003cp\u003e1.8.7 Periodically Perforated Domain 88\u003c\/p\u003e \u003cp\u003e1.8.8 Waves in Periodically Nonhomogenous Media 92\u003c\/p\u003e \u003cp\u003eReferences 95\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Computational Methods for Plates and Beams with Mixed Boundary Conditions 105\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2.1 Introduction 105\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1.1 Computational Methods of Plates with Mixed Boundary Conditions 105\u003c\/p\u003e \u003cp\u003e2.1.2 Method of Boundary Conditions Perturbation 107\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2.2 Natural Vibrations of Beams and Plates 109\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.2.1 Natural Vibrations of a Clamped Beam 109\u003c\/p\u003e \u003cp\u003e2.2.2 Natural Vibration of a Beam with Free Ends 114\u003c\/p\u003e \u003cp\u003e2.2.3 Natural Vibrations of a Clamped Rectangular Plate 118\u003c\/p\u003e \u003cp\u003e2.2.4 Natural Vibrations of the Orthotropic Plate with Free Edges Lying on an Elastic Foundation 123\u003c\/p\u003e \u003cp\u003e2.2.5 Natural Vibrations of the Plate with Mixed Boundary Conditions \"Clamping-Simple Support\" 128\u003c\/p\u003e \u003cp\u003e2.2.6 Comparison of Theoretical and Experimental Results 133\u003c\/p\u003e \u003cp\u003e2.2.7 Natural Vibrations of a Partially Clamped Plate 135\u003c\/p\u003e \u003cp\u003e2.2.8 Natural Vibrations of a Plate with Mixed Boundary Conditions \"Simple Support-Moving Clamping\" 140\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2.3 Nonlinear Vibrations of Rods, Beams and Plates 144\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.3.1 Vibrations of the Rod Embedded in a Nonlinear Elastic Medium 144\u003c\/p\u003e \u003cp\u003e2.3.2 Vibrations of the Beam Lying on a Nonlinear Elastic Foundation 153\u003c\/p\u003e \u003cp\u003e2.3.3 Vibrations of the Membrane on a Nonlinear Elastic Foundation 155\u003c\/p\u003e \u003cp\u003e2.3.4 Vibrations of the Plate on a Nonlinear Elastic Foundation 158\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2.4 SSS of Beams and Plates 160\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.4.1 SSS of Beams with Clamped Ends 160\u003c\/p\u003e \u003cp\u003e2.4.2 SSS of the Beam with Free Edges 163\u003c\/p\u003e \u003cp\u003e2.4.3 SSS of Clamped Plate 166\u003c\/p\u003e \u003cp\u003e2.4.4 SSS of a Plate with Free Edges 170\u003c\/p\u003e \u003cp\u003e2.4.5 SSS of the Plate with Mixed Boundary Conditions \"Clamping–Simple Support\" 172\u003c\/p\u003e \u003cp\u003e2.4.6 SSS of a Plate with Mixed Boundary Conditions \"Free Edge–Moving Clamping\" 180\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2.5 Forced Vibrations of Beams and Plates 184\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.5.1 Forced Vibrations of a Clamped Beam 184\u003c\/p\u003e \u003cp\u003e2.5.2 Forced Vibrations of Beam with Free Edges 189\u003c\/p\u003e \u003cp\u003e2.5.3 Forced Vibrations of a Clamped Plate 190\u003c\/p\u003e \u003cp\u003e2.5.4 Forced Vibrations of Plates with Free Edges 194\u003c\/p\u003e \u003cp\u003e2.5.5 Forced Vibrations of Plate with Mixed Boundary Conditions \"Clamping-Simple Support\" 197\u003c\/p\u003e \u003cp\u003e2.5.6 Forced Vibrations of Plate with Mixed Boundary Conditions \"Free Edge – Moving Clamping\" 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2.6 Stability of Beams and Plates 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.6.1 Stability of a Clamped Beam 207\u003c\/p\u003e \u003cp\u003e2.6.2 Stability of a Clamped Rectangular Plate 209\u003c\/p\u003e \u003cp\u003e2.6.3 Stability of Rectangular Plate with Mixed Boundary Conditions \"Clamping-Simple Support\" 211\u003c\/p\u003e \u003cp\u003e2.6.4 Comparison of Theoretical and Experimental Results 219\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2.7 Some Related Problems 221\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.7.1 Dynamics of Nonhomogeneous Structures 221\u003c\/p\u003e \u003cp\u003e2.7.2 Method of Ishlinskii-Leibenzon 224\u003c\/p\u003e \u003cp\u003e2.7.3 Vibrations of a String Attached to a Spring-Mass-Dashpot System 230\u003c\/p\u003e \u003cp\u003e2.7.4 Vibrations of a String with Nonlinear BCs 233\u003c\/p\u003e \u003cp\u003e2.7.5 Boundary Conditions and First Order Approximation Theory 238\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2.8 Links between the Adomian and Homotopy Perturbation Approaches 240\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2.9 Conclusions 263\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences 264\u003c\/p\u003e \u003cp\u003eIndex 269\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":53186829680983,"sku":"9781118725191","price":98.06,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/asymptotic-methods-in-the-theory-of-plates-with-mixed-boundary-conditions-9781118725191","provider":"Book Curl","version":"1.0","type":"link"}