Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches
Springer Science & Business Media, Jan 5, 2012 - Technology & Engineering - 396 pages
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.
Chapter 1 Introduction
Chapter 2 Perturbation Method LindstedtPoincaré
Chapter 3 The Method of Harmonic Balance
Chapter 4 The Method of Krylov and Bogolyubov
Chapter 5 The Method of Multiple Scales
Chapter 6 The Optimal Homotopy Asymptotic Method
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_ approximate _______ numerical ¼ b ¼ accuracy amplitude analytical results analytical solutions applied approximate frequency approximate results approximate solution Eq auxiliary function Avoiding the presence becomes C1 ¼ coefﬁcients collocation method consider convergence cos Qt š Ž determined Duffing equation dynamical systems exact frequency exact solution ﬁrst-order approximate solution Fourier series fourth-order Runge—Kutta method given by Eq harmonic balance Herisanu homotopy analysis method homotopy asymptotic method homotopy perturbation method initial approximation initial conditions integration results obtained iteration method linear operator Marinca nonlinear differential equation nonlinear dynamical nonlinear dynamical systems nonlinear oscillations nonlinear problems nonlinear systems numerical integration results numerical solution obtain C1 obtain the following obtained from Eq OHAM periodic solution phase plane present solution results of Eq Runge–Kutta method second-order approximate solution secular terms small parameter solution of Eq solutions obtained solving Sound Vib Substituting Eq uštŽ ¼ unknown constants variable vibration