Overview
- Presents exact analytical solutions for second order differential equations of any order of nonlinearity, with many examples
- Features original approximate solving methods for strong nonlinear differential equations
- Also considers strong nonlinear oscillators with one and two degrees of freedom, but also continuous vibrating systems
- Stresses the potential for applications of the method described in engineering
- Contains examples for better learning
- Supplies the mathematical basics in the supplement
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Engineering (MATHENGIN)
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Table of contents (9 chapters)
Keywords
- 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
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 periodicexcitation 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.
Authors and Affiliations
About the author
Livija Cveticanin is Professor of Mechanics and Theory of Machines and Mechanisms. She got her PhD at the University of Novi Sad in Novi Sad, Serbia, and the degree of the Doctor of Hungarian Academy of Sciences in Budapest, Hungary. She published more than 300 papers: more than 120 in the journals which have impact factors and are cited by Scopus and Web of Science. Livija Cveticanin was the lecturer at the CISM International Centre for Mechanical Sciences. The number of citations according to Google Scholar is more than 1800. She is one of the Editors of the journal Mechanism and Machine Theory.
Bibliographic Information
Book Title: Strong Nonlinear Oscillators
Book Subtitle: Analytical Solutions
Authors: Livija Cveticanin
Series Title: Mathematical Engineering
DOI: https://doi.org/10.1007/978-3-319-58826-1
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing AG 2018
Hardcover ISBN: 978-3-319-58825-4Published: 08 June 2017
Softcover ISBN: 978-3-319-86484-6Published: 04 August 2018
eBook ISBN: 978-3-319-58826-1Published: 29 May 2017
Series ISSN: 2192-4732
Series E-ISSN: 2192-4740
Edition Number: 2
Number of Pages: XII, 317
Number of Illustrations: 72 b/w illustrations, 21 illustrations in colour
Topics: Vibration, Dynamical Systems, Control, Mathematical Methods in Physics, Mathematical Applications in the Physical Sciences, Applications of Nonlinear Dynamics and Chaos Theory