Analytical Solutions and Bifurcation of Nonlinear Oscillators with Discontinuities and Impulsive Systems by a Perturbation-incremental Method PDF Download

Author: 汪海玲
Publisher:
ISBN:
Category : Bifurcation theory
Languages : en
Pages : 246

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Author: Livija Cveticanin
Publisher: Springer
ISBN: 3319052721
Category : Science
Languages : en
Pages : 241

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Book Description
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations.

Author: Qingjie Cao
Publisher: Springer
ISBN: 3662530945
Category : Technology & Engineering
Languages : en
Pages : 273

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Book Description
This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

Author: Jan Awrejcewicz
Publisher: World Scientific
ISBN: 9814522910
Category : Science
Languages : en
Pages : 257

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This book develops a general methodological approach to investigate complex physical systems presented by the author in a previous book. The nonlinear dynamics of coupled oscillators is investigated numerically and analytically. Three different mechanical, and one biomechanical, examples are used to demonstrate a general systematical approach to the study of dissipative dynamical systems. Many original examples of special chaotic behavior are discussed and illustrated.

Author: J. Chandra
Publisher: Elsevier
ISBN: 0080871917
Category : Mathematics
Languages : en
Pages : 133

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Coupled Nonlinear Oscillators

Author: Alvaro Humberto Salas
Publisher:
ISBN:
Category : Electronic books
Languages : en
Pages : 0

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Oscillators are omnipresent; most of them are inherently nonlinear. Though a nonlinear equation mostly does not yield an exact analytic solution for itself, plethora of elementary yet practical techniques exist for extracting important information about the solution of equation. The purpose of this chapter is to introduce some new techniques for the readers which are carefully illustrated using mainly the examples of Duffing,Äôs oscillator. Using the exact analytical solution to cubic Duffing and cubic-quinbic Duffing oscillators, we describe the way other conservative and some non conservative damped nonlinear oscillators may be studied using analytical techniques described here. We do not make use of perturbation techniques. However, some comparison with such methods are performed. We consider oscillators having the form x¬®+fx=0 as well as x¬®+2ŒμxÃá+fx=Ft, where x=xt and f=fx and Ft are continuous functions. In the present chapter, sometimes we will use f,àíx=,àífx and take the approximation fx,âà,àëj=1Npjxj, where j=1,3,5,,ãØN only odd integer values and x,àà,àíAA. Moreover, we will take the approximation fx,âà,àëj=0Npjxj, where j=1,2,3,,ãØN, and x,àà,àíAA. Arbitrary initial conditions are considered. The main idea is to approximate the function f=fx by means of some suitable cubic or quintic polynomial. The analytical solutions are expressed in terms of the Jacobian and Weierstrass elliptic functions. Applications to plasma physics, electronic circuits, soliton theory, and engineering are provided.

Author: Muthusamy Lakshmanan
Publisher: World Scientific
ISBN: 9789810221430
Category : Science
Languages : en
Pages : 346

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Book Description
This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.

Author: Gerhard Dangelmayr
Publisher: World Scientific
ISBN: 9812567844
Category : Mathematics
Languages : en
Pages : 405

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Book Description
Understanding the spontaneous formation and dynamics of spatiotemporal patterns in dissipative nonequilibrium systems is one of the major challenges in nonlinear science. This collection of expository papers and advanced research articles, written by leading experts, provides an overview of the state of the art. The topics include new approaches to the mathematical characterization of spatiotemporal complexity, with special emphasis on the role of symmetry, as well as analysis and experiments of patterns in a remarkable variety of applied fields such as magnetoconvection, liquid crystals, granular media, Faraday waves, multiscale biological patterns, visual hallucinations, and biological pacemakers. The unitary presentations, guiding the reader from basic fundamental concepts to the most recent research results on each of the themes, make the book suitable for a wide audience.

Author: Livija Cveticanin
Publisher: Springer
ISBN: 9783319588254
Category : Technology & Engineering
Languages : en
Pages : 0

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Book Description
This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author’s original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear oscillators is enlarged and a variety of procedures for solving free strong nonlinear oscillators is suggested. A method for error estimation is also given which is suitable to compare the exact and approximate solutions. Besides the oscillators with one degree-of-freedom, the one and two mass oscillatory systems with two-degrees-of-freedom and continuous oscillators are considered. The chaos and chaos suppression in ideal and non-ideal mechanical systems is explained. In this second edition more attention is given to the application of the suggested methodologies and obtained results to some practical problems in physics, mechanics, electronics and biomechanics. Thus, for the oscillator with two degrees-of-freedom, a generalization of the solving procedure is performed. Based on the obtained results, vibrations of the vocal cord are analyzed. In the book the vibration of the axially purely nonlinear rod as a continuous system is investigated. The developed solving procedure and the solutions are applied to discuss the muscle vibration. Vibrations of an optomechanical system are analyzed using the oscillations of an oscillator with odd or even quadratic nonlinearities. The extension of the forced vibrations of the system is realized by introducing the Ateb periodic excitation force which is the series of a trigonometric function. The book is self-consistent and suitable for researchers and as a textbook for students and also professionals and engineers who apply these techniques to the field of nonlinear oscillations.

Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 348

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Book Description