Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Andrianov, Igorʹ Vasilʹevich (1948-....)
Titre(s) : Asymptotic methods in the theory of plates with mixed boundary conditions [Texte électronique] / Igor Andrianov, Jan Awrejcewicz, Vladislav V. Danishevskyy, Andrey O. Ivankov
Publication : Chichester, West Sussex, United Kingdom : John Wiley & Sons, Ltd., 2014
Description matérielle : 1 online resource
Note(s) : Includes bibliographical references and index. - Print version record and CIP data provided by publisher.
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.
Autre(s) auteur(s) : Awrejcewicz, Jan. Fonction indéterminée
Danishevskiĭ, Vladislav Valentinovich. Fonction indéterminée
Ivankov, Andrey. Fonction indéterminée
Sujet(s) : Plaques (ingénierie) -- Modèles mathématiques
Développements asymptotiques
Éléments finis, Méthode des
Identifiants, prix et caractéristiques : ISBN 9781118725184
Identifiant de la notice : ark:/12148/cb44654901w
Notice n° :
FRBNF44654901
(notice reprise d'un réservoir extérieur)
Table des matières : 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.
