Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches

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Springer Science & Business Media, Jan 5, 2012 - Technology & Engineering - 396 pages
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This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part.
Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.
 

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Contents

Introduction
1
Perturbation Method LindstedtPoincaré
9
The Method of Harmonic Balance
31
The Method of Krylov and Bogolyubov
46
The Method of Multiple Scales
83
The Optimal Homotopy Asymptotic Method
103
The Optimal Homotopy Perturbation Method
211
The Optimal Variational Iteration Method
259
Optimal Parametric Iteration Method
313
References
385
Index
393
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