Strong Nonlinear Oscillators

Analytical Solutions

  • Livija Cveticanin

Part of the Mathematical Engineering book series (MATHENGIN)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Livija Cveticanin
    Pages 1-3
  3. Livija Cveticanin
    Pages 5-15
  4. Livija Cveticanin
    Pages 17-49
  5. Livija Cveticanin
    Pages 51-117
  6. Livija Cveticanin
    Pages 119-158
  7. Livija Cveticanin
    Pages 159-196
  8. Livija Cveticanin
    Pages 197-245
  9. Livija Cveticanin
    Pages 247-277
  10. Livija Cveticanin
    Pages 279-296
  11. Back Matter
    Pages 297-317

About this book


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.  


Free Strong Nonlinear Oscillator Forced Strong Nonlinear Oscillator Purely Nonlinear Oscillator Axial Vibration of Strong Nonlinear Rod Vocal Cord Vibration Chaos in Oscillators Deterministic Chaos Non-ideal Mechanical System Oscillators with Time-Variable Parameters Solving Nonlinear Oscillator Equations Two-Degree-Of-Freedom Oscillator Waves and Oscillations Opto-Mechanical Oscillator

Authors and affiliations

  • Livija Cveticanin
    • 1
  1. 1.Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-58825-4
  • Online ISBN 978-3-319-58826-1
  • Series Print ISSN 2192-4732
  • Series Online ISSN 2192-4740
  • Buy this book on publisher's site
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