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Titlebook: Nonlinear Dynamical Systems in Engineering; Some Approximate App Vasile Marinca,Nicolae Herisanu Book 2011 Springer-Verlag Berlin Heidelber

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书目名称Nonlinear Dynamical Systems in Engineering
副标题Some Approximate App
编辑Vasile Marinca,Nicolae Herisanu
视频video
概述Provides a better understanding of the base functions and the auxialiary functions for optimal approaches.Inspires to appreciate the beauty as well as the usefulness of the optimal analytical techniqu
图书封面Titlebook: Nonlinear Dynamical Systems in Engineering; Some Approximate App Vasile Marinca,Nicolae Herisanu Book 2011 Springer-Verlag Berlin Heidelber
描述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.
出版日期Book 2011
关键词Harmonic balance; Krylov and Bogolyubov method of; Lindstedt-Poincaré; Multiple scales; auxiliary funct
版次1
doihttps://doi.org/10.1007/978-3-642-22735-6
isbn_softcover978-3-642-43410-5
isbn_ebook978-3-642-22735-6
copyrightSpringer-Verlag Berlin Heidelberg 2011
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https://doi.org/10.1007/978-3-642-22735-6Harmonic balance; Krylov and Bogolyubov method of; Lindstedt-Poincaré; Multiple scales; auxiliary funct
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Introduction,Most nonlinear phenomena are models of our real-life problems. The world around us is inherently nonlinear. A vast body of scientific knowledge has developed over a long period of time, devoted to a description of natural phenomena.
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,Perturbation Method: Lindstedt-Poincaré,We seek an expansion that is valid for small but finite amplitude motions. It is convenient to introduce a small, dimensionless parameter e which is of the order of the amplitude of the motion and can be used as a crutch, or a bookkeeping device, in obtaining the approximate solution [22,33–35].
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The Method of Harmonic Balance,This method may be used to determine the approximate periodic solutions of nonlinear differential equations. If a periodic solution does exist, it may be sought in the form of a Fourier series, whose coefficients are determined by requiring the series to satisfy the equation of motion.
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Optimal Parametric Iteration Method,The most common and most widely studied methods for determining analytical approximate solutions of a nonlinear dynamical system are iteration methods.
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