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.
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_ approximate _______ numerical ¼ b ¼ accuracy amplitude analytical solutions applications approximate results approximate solution Eq auxiliary function Avoiding the presence becomes C1 ¼ C2 ¼ coefficients collocation method consider convergence cos3t cost ð Þ 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 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 numerical integration results numerical results numerical solution obtain C1 obtain the following obtained from Eq OHAM periodic solution phase plane present solution respectively results of Eq second-order approximate solution secular terms small parameter solution of Eq solutions obtained solving Sound Vib Substituting Eq term in Eq uðtÞ ¼ unknown constants variable vibration