Strongly Nonlinear Oscillators
Analytical Solutions
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Beschreibung
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.
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.
Provides the unique analytical solving procedure for any strong nonlinear oscillator Includes many examples for practical applications Discusses chaos in ideal and nonlinear pure nonlinear oscillators Supports learning with end-of-chapter exercises and a solution manual Includes supplementary material: sn.pub/extras
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Themen in »Strongly Nonlinear Oscillators«
Chaos in Oscillators Deterministic Chaos Non-ideal Mechanical System Oscillators with Time-Variable Parameters Solving Nonlinear Oscillator Equations Strong Nonlinear Vibration Two-Degree-Of-Freedom Oscillator Waves and Oscillations
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From the book reviews:
“This book is devoted to analysis of solutions of the second-order ordinary differential equations (or systems) which describe oscillations of mechanical (and related) systems. … the book can be recommended to engineers as a good source of methods and examples.” (Henryk Żołądek, Mathematical Reviews, January, 2015)
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