Record Nr.

UNINA9910130873903321

Titolo

The Duffing equation [[electronic resource] ] : nonlinear oscillators and their behaviour / / edited by Ivana Kovacic, Michael J. Brennan

Pubbl/distr/stampa


Chichester, West Sussex, : Wiley, 2011

ISBN

0-470-97783-3

1-283-37306-8

9786613373069

0-470-97786-8

0-470-97785-X

Descrizione fisica

1 online resource (392 p.)

Altri autori (Persone)

BrennanMichael J <1956-> (Michael John)

KovacicIvana <1972->

Disciplina

515.35

515/.35

620.001515355

Soggetti

Duffing equations

Nonlinear oscillators - Mathematical models

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

The Duffing Equation: Nonlinear Oscillators and their Behaviour; Contents; Contributors; Preface; 1 Background: On Georg Duffing and the Duffing equation; 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; 1.5.1 Description of Duffing's book; 1.5.2 Reviews of Duffing's book; 1.6 Research inspired by Duffing's work; 1.6.1 1918-1952; 1.6.2 1962 to the present day; 1.7 Some other books on nonlinear dynamics; 1.8 Overview of this book; References

2 Examples of physical systems described by the Duffing equation2.1 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; 2.7.1 Quasi-zero stiffness 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; 2.11.1 The electrical circuit studied by Ueda; 2.12 Summary; References

3 Free vibration of a Duffing oscillator with viscous damping3.1 Introduction; 3.2 Fixed points and their stability; 3.2.1 Case when the nontrivial fixed points do not exist (αγ > 0); 3.2.2 Case when the nontrivial fixed points exist (αγ < 0); 3.2.3 Variation of phase portraits depending on linear stiffness and linear damping; 3.3 Local bifurcation analysis; 3.3.1 Bifurcation from trivial fixed points; 3.3.2 Bifurcation from nontrivial fixed points; 3.4 Global analysis for softening nonlinear stiffness (γ < 0); 3.4.1 Phase portraits; 3.4.2 Global bifurcation analysis

3.5 Global analysis for hardening nonlinear stiffness (γ > 0)3.5.1 Phase portraits; 3.5.2 Global bifurcation analysis; 3.6 Summary; Acknowledgments; References; 4 Analysis techniques for the various forms of the Duffing equation; 4.1 Introduction; 4.2 Exact solution for free oscillations of the Duffing equation with cubic nonlinearity; 4.2.1 The frequency and period of free oscillations of the Duffing oscillator; 4.2.2 Discussion; 4.3 The elliptic harmonic balance method; 4.3.1 The Duffing equation with a strong quadratic term; 4.3.2 The Duffing equation with damping

4.3.3 The harmonically excited Duffing oscillator4.3.4 The harmonically excited pure cubic Duffing equation; 4.4 The elliptic Galerkin method; 4.4.1 Duffing oscillator with a strong excitation force of elliptic type; 4.5 The straightforward expansion method; 4.5.1 The Duffing equation with a small quadratic term; 4.6 The elliptic Lindstedt-Poincaré method; 4.6.1 The Duffing equation with a small quadratic term; 4.7 Averaging methods; 4.7.1 The generalised elliptic averaging method; 4.7.2 Elliptic Krylov-Bogolubov (EKB) method for the pure cubic Duffing oscillator

4.8 Elliptic homotopy methods

Sommario/riassunto

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 mathem

Record Nr.

UNISA996204456403316

Titolo

Proceedings of the Intelligent Vehicles '93 Symposium : September 25-26, 1995, Detroit, USA / / sponsored by IEEE Industrial Electronics Society

Pubbl/distr/stampa


Piscataway, New Jersey : , : Institute of Electrical and Electronics Engineers, , 1995

Descrizione fisica

1 online resource (536 pages)

Disciplina

629.283

Soggetti

Automobile driving - Automation

Automobiles - Automatic control

Intelligent transportation systems