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Asymptotic methods in the theory of plates with mixed boundary conditions /
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 prob...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Chichester, West Sussex, United Kingdom :
John Wiley & Sons, Ltd.,
2014.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
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| 100 | 1 | |a Andrianov, I. V. |q (Igorʹ Vasilʹevich), |d 1948- | |
| 245 | 1 | 0 | |a Asymptotic methods in the theory of plates with mixed boundary conditions / |c Igor Andrianov, Jan Awrejcewicz, Vladislav V. Danishevskyy, Andrey O. Ivankov. |
| 264 | 1 | |a Chichester, West Sussex, United Kingdom : |b John Wiley & Sons, Ltd., |c 2014. | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record and CIP data provided by publisher. | |
| 520 | |a 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. -- |c Edited summary from book. | ||
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Plates (Engineering) |x Mathematical models. | |
| 650 | 0 | |a Asymptotic expansions. | |
| 650 | 6 | |a Plaques (Ingénierie) |x Modèles mathématiques. | |
| 650 | 6 | |a Développements asymptotiques. | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING |x Civil |x General. |2 bisacsh | |
| 650 | 7 | |a Asymptotic expansions |2 fast | |
| 650 | 7 | |a Plates (Engineering) |x Mathematical models |2 fast | |
| 700 | 1 | |a Awrejcewicz, J. |q (Jan) | |
| 700 | 1 | |a Danishevskiĭ, V. V. |q (Vladislav Valentinovich) | |
| 700 | 1 | |a Ivankov, Andrey. | |
| 776 | 0 | 8 | |i Print version: |a Andrianov, I.V. (Igorʹ Vasilʹevich), 1948- |t Asymptotic methods in the theory of plates with mixed boundary conditions. |d Chichester, West Sussex, United Kingdom : John Wiley & Sons, Ltd., 2014 |z 9781118725191 |w (DLC) 2013034287 |
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