Strongly Nonlinear Oscillators: Analytical Solutions

✍ Scribed by Livija Cveticanin (auth.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 241
• Series: Undergraduate Lecture Notes in Physics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-ix
Introduction....Pages 1-3
Nonlinear Oscillators....Pages 5-15
Pure Nonlinear Oscillator....Pages 17-48
Free Vibrations....Pages 49-85
Oscillators with Time Variable Parameters....Pages 87-126
Forced Vibrations....Pages 127-160
Two-Degree-of-Freedom Oscillator....Pages 161-189
Chaos in Oscillators....Pages 191-221
Back Matter....Pages 223-239

✦ Subjects

Nonlinear Dynamics; Appl.Mathematics/Computational Methods of Engineering; Mathematical Applications in the Physical Sciences; Mathematical Methods in Physics; Vibration, Dynamical Systems, Control