LEADER 05477nam 2200649 450 001 9910823739903321 005 20230803195221.0 010 $a1-118-72514-X 010 $a1-118-72518-2 010 $a1-118-72513-1 035 $a(CKB)2670000000523230 035 $a(EBL)1631084 035 $a(SSID)ssj0001111365 035 $a(PQKBManifestationID)11591188 035 $a(PQKBTitleCode)TC0001111365 035 $a(PQKBWorkID)11130714 035 $a(PQKB)10003377 035 $a(OCoLC)870589263 035 $a(MiAaPQ)EBC1631084 035 $a(DLC) 2013035003 035 $a(Au-PeEL)EBL1631084 035 $a(CaPaEBR)ebr10837065 035 $a(EXLCZ)992670000000523230 100 $a20140219h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aAsymptotic methods in the theory of plates with mixed boundary conditions /$fIgor V. Andrianov [and three others] 210 1$aChichester, England :$cWiley,$d2014. 210 4$dİ2014 215 $a1 online resource (288 p.) 300 $aDescription based upon print version of record. 311 $a1-118-72519-0 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aCover; Title Page; Copyright; Contents; Preface; List of Abbreviations; Chapter 1 Asymptotic Approaches; 1.1 Asymptotic Series and Approximations; 1.1.1 Asymptotic Series; 1.1.2 Asymptotic Symbols and Nomenclatures; 1.2 Some Nonstandard Perturbation Procedures; 1.2.1 Choice of Small Parameters; 1.2.2 Homotopy Perturbation Method; 1.2.3 Method of Small Delta; 1.2.4 Method of Large Delta; 1.2.5 Application of Distributions; 1.3 Summation of Asymptotic Series; 1.3.1 Analysis of Power Series; 1.3.2 Pade? Approximants and Continued Fractions; 1.4 Some Applications of PA 327 $a1.4.1 Accelerating Convergence of Iterative Processes1.4.2 Removing Singularities and Reducing the Gibbs-Wilbraham Effect; 1.4.3 Localized Solutions; 1.4.4 Hermite-Pade? Approximations and Bifurcation Problem; 1.4.5 Estimates of Effective Characteristics of Composite Materials; 1.4.6 Continualization; 1.4.7 Rational Interpolation; 1.4.8 Some Other Applications; 1.5 Matching of Limiting Asymptotic Expansions; 1.5.1 Method of Asymptotically Equivalent Functions for Inversion of Laplace Transform; 1.5.2 Two-Point PA; 1.5.3 Other Methods of AEFs Construction; 1.5.4 Example: Schro?dinger Equation 327 $a1.5.5 Example: AEFs in the Theory of Composites1.6 Dynamical Edge Effect Method; 1.6.1 Linear Vibrations of a Rod; 1.6.2 Nonlinear Vibrations of a Rod; 1.6.3 Nonlinear Vibrations of a Rectangular Plate; 1.6.4 Matching of Asymptotic and Variational Approaches; 1.6.5 On the Normal Forms of Nonlinear Vibrations of Continuous Systems; 1.7 Continualization; 1.7.1 Discrete and Continuum Models in Mechanics; 1.7.2 Chain of Elastically Coupled Masses; 1.7.3 Classical Continuum Approximation; 1.7.4 ""Splashes''; 1.7.5 Envelope Continualization; 1.7.6 Improvement Continuum Approximations 327 $a1.7.7 Forced Oscillations1.8 Averaging and Homogenization; 1.8.1 Averaging via Multiscale Method; 1.8.2 Frozing in Viscoelastic Problems; 1.8.3 The WKB Method; 1.8.4 Method of Kuzmak-Whitham (Nonlinear WKB Method); 1.8.5 Differential Equations with Quickly Changing Coefficients; 1.8.6 Differential Equation with Periodically Discontinuous Coefficients; 1.8.7 Periodically Perforated Domain; 1.8.8 Waves in Periodically Nonhomogenous Media; References; Chapter 2 Computational Methods for Plates and Beams with Mixed Boundary Conditions; 2.1 Introduction 327 $a2.1.1 Computational Methods of Plates with Mixed Boundary Conditions2.1.2 Method of Boundary Conditions Perturbation; 2.2 Natural Vibrations of Beams and Plates; 2.2.1 Natural Vibrations of a Clamped Beam; 2.2.2 Natural Vibration of a Beam with Free Ends; 2.2.3 Natural Vibrations of a Clamped Rectangular Plate; 2.2.4 Natural Vibrations of the Orthotropic Plate with Free Edges Lying on an Elastic Foundation; 2.2.5 Natural Vibrations of the Plate with Mixed Boundary Conditions ""Clamping-Simple Support''; 2.2.6 Comparison of Theoretical and Experimental Results 327 $a2.2.7 Natural Vibrations of a Partially Clamped Plate 330 $a Covers the theoretical background of asymptotic approaches and its applicability to solve mechanical engineering-oriented problems of plates with mixed boundary conditions Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions comprehensively covers the theoretical background of asymptotic approaches and its applicability to solve mechanical engineering-oriented problems of structural members, primarily plates (statics and dynamics) with mixed boundary conditions.The first part of this book is devoted to the description of asymptotic method 606 $aPlates (Engineering)$xMathematical models 606 $aAsymptotic expansions 615 0$aPlates (Engineering)$xMathematical models. 615 0$aAsymptotic expansions. 676 $a624.1/7765015114 700 $aAndrianov$b I. V$g(Igor? Vasil?evich),$f1948-$01598069 701 $aAndrianov$b I. V$g(Igor? Vasil?evich),$f1948-$01598069 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910823739903321 996 $aAsymptotic methods in the theory of plates with mixed boundary conditions$93920087 997 $aUNINA