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Mathematical Engineering

Strong Nonlinear Oscillators

Analytical Solutions

Authors: Cveticanin, Livija

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  • 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 
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eBook 117,69 €
price for Spain (gross)
  • ISBN 978-3-319-58826-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 155,99 €
price for Spain (gross)
  • ISBN 978-3-319-58825-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 155,99 €
price for Spain (gross)
  • ISBN 978-3-319-86484-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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.  

About the authors

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.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook 117,69 €
price for Spain (gross)
  • ISBN 978-3-319-58826-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 155,99 €
price for Spain (gross)
  • ISBN 978-3-319-58825-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 155,99 €
price for Spain (gross)
  • ISBN 978-3-319-86484-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Strong Nonlinear Oscillators
Book Subtitle
Analytical Solutions
Authors
Series Title
Mathematical Engineering
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-58826-1
DOI
10.1007/978-3-319-58826-1
Hardcover ISBN
978-3-319-58825-4
Softcover ISBN
978-3-319-86484-6
Series ISSN
2192-4732
Edition Number
2
Number of Pages
XII, 317
Number of Illustrations
72 b/w illustrations, 21 illustrations in colour
Topics