Ebook: Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches

This book presents and extends 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 various fields of engineering.

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This book presents and extends 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 various fields of engineering.

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This book presents and extends 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 various fields of engineering.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-8
Perturbation Method: Lindstedt-Poincar?....Pages 9-29
The Method of Harmonic Balance....Pages 31-45
The Method of Krylov and Bogolyubov....Pages 47-82
The Method of Multiple Scales....Pages 83-102
The Optimal Homotopy Asymptotic Method....Pages 103-209
The Optimal Homotopy Perturbation Method....Pages 211-257
The Optimal Variational Iteration Method....Pages 259-311
Optimal Parametric Iteration Method....Pages 313-384
Back Matter....Pages 385-395

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This book presents and extends 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 various fields of engineering.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-8
Perturbation Method: Lindstedt-Poincar?....Pages 9-29
The Method of Harmonic Balance....Pages 31-45
The Method of Krylov and Bogolyubov....Pages 47-82
The Method of Multiple Scales....Pages 83-102
The Optimal Homotopy Asymptotic Method....Pages 103-209
The Optimal Homotopy Perturbation Method....Pages 211-257
The Optimal Variational Iteration Method....Pages 259-311
Optimal Parametric Iteration Method....Pages 313-384
Back Matter....Pages 385-395
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