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

Chapter 1 Introduction
1
Chapter 2 Perturbation Method LindstedtPoincaré
9
Chapter 3 The Method of Harmonic Balance
31
Chapter 4 The Method of Krylov and Bogolyubov
46
Chapter 5 The Method of Multiple Scales
83
Chapter 6 The Optimal Homotopy Asymptotic Method
103
Chapter 7 The Optimal Homotopy Perturbation Method
211
Chapter 8 The Optimal Variational Iteration Method
259
Chapter 9 Optimal Parametric Iteration Method
313
References
385
Index
393
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