05296nam 2200649Ia 450 991087686920332120200520144314.00-470-97783-31-283-37306-897866133730690-470-97786-80-470-97785-X(CKB)3460000000000110(EBL)661779(OCoLC)742333156(SSID)ssj0000476926(PQKBManifestationID)11326949(PQKBTitleCode)TC0000476926(PQKBWorkID)10502073(PQKB)10555481(MiAaPQ)EBC661779(EXLCZ)99346000000000011020100901d2011 uy 0engur|n|---|||||txtccrThe Duffing equation nonlinear oscillators and their behaviour /edited by Ivana Kovacic, Michael J. BrennanChichester, West Sussex Wiley20111 online resource (392 p.)Description based upon print version of record.0-470-71549-9 Includes bibliographical references and index.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; References2 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; References3 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 analysis3.5 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 damping4.3.3 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 oscillator4.8 Elliptic homotopy methodsThe 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 mathemDuffing equationsNonlinear oscillatorsMathematical modelsDuffing equations.Nonlinear oscillatorsMathematical models.515.35515/.35620.001515355Brennan Michael J(Michael John),1956-1762454Kovacic Ivana1972-1762455MiAaPQMiAaPQMiAaPQBOOK9910876869203321The Duffing equation4202425UNINA