Nonlinear Oscillations

1. Front Matter

   Pages i-x

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2. Oscillators and Oscillatory Responses in Practical and Theoretical Systems

   • Ivana Kovacic

   Pages 1-17

3. Free Conservative Oscillators: From Linear to Nonlinear Systems

   • Ivana Kovacic

   Pages 19-76

4. Free Damped Oscillators

   • Ivana Kovacic

   Pages 77-132

5. Forced Oscillators

   • Ivana Kovacic

   Pages 133-187

6. Nonlinear Isochronous Oscillators

   • Ivana Kovacic

   Pages 189-222

7. From Chains of Nonlinear Oscillators to Continuous Nonlinear Systems

   • Ivana Kovacic

   Pages 223-259

8. Back Matter

   Pages 261-273

   PDF

This book presents exact, closed-form solutions for the response of a variety of nonlinear oscillators (free, damped, forced). The solutions presented are expressed in terms of special functions. To help the reader understand these `non-standard' functions, detailed explanations and rich illustrations of their meanings and contents are provided. In addition, it is shown that these exact solutions in certain cases comprise the well-known approximate solutions for some nonlinear oscillations.

• Hardening Duffing oscillators
• Softening Duffing oscillators
• Quadratic oscillators
• Isochronous oscillators
• Jacobi elliptic functions
• Purely nonlinear oscillators

“The book is well written and very easy to read. From the first pages, where the reader finds the motivation, it is an engaging and informatively very beneficial reading. The connection of mechanics and mathematics is described as well. The text is complemented by illustrative pictures.” (Petr Hasil, Mathematical Reviews, October, 2022)

• Faculty of Technical Sciences, Centre for Vibro-Acoustic Systems and Signal Processing, University of Novi Sad, Novi Sad, Serbia

  Ivana Kovacic

Ivana Kovacic is a Full Professor of Mechanics at the Faculty of Technical Sciences, University of Novi Sad, Serbia, and the Head of the Centre for Vibro-Acoustic Systems and Signal Processing CEVAS at the same faculty. Her research involves the use of quantitative and qualitative methods to study governing equations arising from nonlinear dynamics problems. She is the editor/author of the books ‘The Duffing Equation: Nonlinear Oscillators and their Behaviour’ and ‘Mechanical Vibrations: Fundamentals with Solved Examples’ (both published by Wiley) as well as two textbooks in Serbian. She is a Subject Editor in three academic journals: Journal of Sound and Vibration (Elsevier), Mechanics Research Communications (Elsevier) and Meccanica (Springer). 

 

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