The Duffing Equation: Nonlinear Oscillators and their
Behaviour brings together the results of a wealth of
disseminated research literature on the Duffing equation, a key
engineering model with a vast number of applications in science and
engineering, summarizing the findings of this research. Each
chapter is written by an expert contributor in the field of
nonlinear dynamics and addresses a different form of the equation,
relating it to various oscillatory problems and clearly linking the
problem with the mathematics that describe it. The editors and the
contributors explain the mathematical techniques required to study
nonlinear dynamics, helping the reader with little mathematical
background to understand the text.
The Duffing Equation provides a reference text for
postgraduate and students and researchers of mechanical engineering
and vibration / nonlinear dynamics as well as a useful tool for
practising mechanical engineers.
* Includes a chapter devoted to historical background on Georg
Duffing and the equation that was named after him.
* Includes a chapter solely devoted to practical examples of
systems whose dynamic behaviour is described by the Duffing
equation.
* Contains a comprehensive treatment of the various forms of the
Duffing equation.
* Uses experimental, analytical and numerical methods as well as
concepts of nonlinear dynamics to treat the physical systems in a
unified way.
Autorentext
Michael J Brennan, Dynamics Group, Institute of Sound and Vibration Research (ISVR), University of Southampton, UK
Professor Michael Brennan holds a personal chair in Engineering Dynamics and is Chairman of the Dynamics Research in the ISVR at Southampton University. He joined Southampton in 1995 after a 23 year career as an engineer in the Royal Navy. Since 1995 Professor Brennan has worked on several aspects of sound and vibration, specialising in the use of smart structures for active vibration control, active control of structurally-radiated sound and the condition monitoring of gear boxes by the analysis of vibration data and rotor dynamics. Mike Brennan has edited 3 conference proceedings, 3 book chapters, and over 200 academic journal and conference papers.
Ivana Kovavic, Department of Mathematics, Faculty of Technical Sciences, University of Novi Sad, Serbia Ivana
Kovavic is an associate professor within the Department of Mathematics at the University of Novi Sad in Serbia. She has authored two books in the Polish language, 30 journal and conference papers and edited 1 conference proceedings.
Klappentext
The Duffing Equation: Nonlinear Oscillators and their Behaviour
Ivana Kovacic, University of Novi Sad, Faculty of Technical Sciences, Serbia
Michael J Brennan, University of Southampton, Institute of Sound and Vibration Research, United Kingdom
The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical techniques required to study nonlinear dynamics, helping the reader with little mathematical background to understand the text.
The Duffing Equation provides a reference text for postgraduate and students and researchers of mechanical engineering and vibration / nonlinear dynamics as well as a useful tool for practising mechanical engineers.
- Includes a chapter devoted to historical background on Georg Duffing and the equation that was named after him.
- Includes a chapter solely devoted to practical examples of systems whose dynamic behaviour is described by the Duffing equation.
- Contains a comprehensive treatment of the various forms of the Duffing equation.
- Uses experimental, analytical and numerical methods as well as concepts of nonlinear dynamics to treat the physical systems in a unified way.
Zusammenfassung
The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical techniques required to study nonlinear dynamics, helping the reader with little mathematical background to understand the text.
The Duffing Equation provides a reference text for postgraduate and students and researchers of mechanical engineering and vibration / nonlinear dynamics as well as a useful tool for practising mechanical engineers.
- Includes a chapter devoted to historical background on Georg Duffing and the equation that was named after him.
- Includes a chapter solely devoted to practical examples of systems whose dynamic behaviour is described by the Duffing equation.
- Contains a comprehensive treatment of the various forms of the Duffing equation.
- Uses experimental, analytical and numerical methods as well as concepts of nonlinear dynamics to treat the physical systems in a unified way.
Inhalt
List of Contributors.
Preface.
1 Background: On Georg Duffing and the Duffing Equation (Ivana Kovacic and Michael J. Brennan).
1.1 Introduction.
1.2 Historical perspective.
1.3 A brief biography of Georg Duffing.
1.4 The work of Georg Duffing.
1.5 Contents of Duffing's book.
1.6 Research inspired by Duffing's work.
1.7 Some other books on nonlinear dynamics.
1.8 Overview of this book.
References.
2 Examples of Physical Systems Described by the Duffing Equation (Michael J. Brennan and Ivana Kovacic).
2.1 Introduction.
2.2 Nonlinear stiffness.
2.3 The pendulum.
2.4 Example of geometrical nonlinearity.
2.5 A system consisting of the pendulum and nonlinear stiffness.
2.6 Snap-through mechanism.
2.7 Nonlinear isolator.
2.8 Large deflection of a beam with nonlinear stiffness.
2.9 Beam with nonlinear stiffness due to inplane tension.
2.10 Nonlinear cable vibrations.
2.11 Nonlinear electrical circuit.
2.12 Summary.
References.
3 Free Vibration of a Duffing Oscillator with Viscous Damping (Hiroshi Yabuno).
3.1 Introduction.
3.2 Fixed points and their stability.
3.3 Local bifurcation analysis.
3.4 Global analysis for softening nonlinear stiffness ( < 0).
3.5 Global analysis for hardening nonlinear stiffness ( < 0).
3.6 Summary.
Acknowledgments.
References.
4 Analysis Techniques for the Various Forms of the Duffing Equation (Livija Cveticanin).
4.1 Introduction.
4.2 Exact solution for free oscillations of the Duffing equation with cubic nonlinearity.
4.3 The elliptic harmonic balance method.
4.4 The elliptic Galerkin method.
4.5 The straightforward expansion method.
4.6 The elliptic Li…