Andrianov, I. V. (Igorʹ Vasilʹevich) 1948- creator Awrejcewicz, J. (Jan) Danishevskiĭ, V. V. (Vladislav Valentinovich) Ivankov, Andrey. text bibliography Electronic books. enk 2014 monographic eng

electronic resource

1 online resource. This book 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. Key features: Includes analytical solving of mixed boundary value problems; Introduces modern asymptotic and summation procedures; Presents asymptotic approaches for nonlinear dynamics of rods, beams and plates; Covers statics, dynamics and stability of plates with mixed boundary conditions; Explains links between the Adomian and homotopy perturbation approaches. This is a comprehensive reference for researchers and practitioners working in the field of Mechanics of Solids and Mechanical Engineering, and is also a valuable resource for graduate and postgraduate students from Civil and Mechanical Engineering. -- Cover; 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 Padé Approximants and Continued Fractions; 1.4 Some Applications of PA. 1.4.1 Accelerating Convergence of Iterative Processes1.4.2 Removing Singularities and Reducing the Gibbs-Wilbraham Effect; 1.4.3 Localized Solutions; 1.4.4 Hermite-Padé 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: Schrödinger Equation. 1.5.5 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. 1.7.7 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. 2.1.1 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. Igor Andrianov, Jan Awrejcewicz, Vladislav V. Danishevskyy, Andrey O. Ivankov. Includes bibliographical references and index. Plates (Engineering) Mathematical models Asymptotic expansions Asymptotic expansions Finite element method Plates (Engineering) Mathematical models Plates (Engineering) TECHNOLOGY & ENGINEERING Civil General Asymptotic expansions Plates (Engineering) Mathematical models TA660.P6 624.1/7765015114 Andrianov, I.V. (Igorʹ Vasilʹevich), 1948- Chichester, West Sussex, United Kingdom : John Wiley & Sons, Ltd., 2014 (DLC) 2013034287 9781118725139 1118725131 9781118725146 111872514X 9781118725184 1118725182 1118725190 9781118725191 2013035003 http://onlinelibrary.wiley.com/book/10.1002/9781118725184 http://onlinelibrary.wiley.com/book/10.1002/9781118725184 DLC 130827 20171106092117.0 ocn857234462 eng