LEADER 05296nam 2200649Ia 450 001 9910876869203321 005 20200520144314.0 010 $a0-470-97783-3 010 $a1-283-37306-8 010 $a9786613373069 010 $a0-470-97786-8 010 $a0-470-97785-X 035 $a(CKB)3460000000000110 035 $a(EBL)661779 035 $a(OCoLC)742333156 035 $a(SSID)ssj0000476926 035 $a(PQKBManifestationID)11326949 035 $a(PQKBTitleCode)TC0000476926 035 $a(PQKBWorkID)10502073 035 $a(PQKB)10555481 035 $a(MiAaPQ)EBC661779 035 $a(EXLCZ)993460000000000110 100 $a20100901d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 04$aThe Duffing equation $enonlinear oscillators and their behaviour /$fedited by Ivana Kovacic, Michael J. Brennan 210 $aChichester, West Sussex $cWiley$d2011 215 $a1 online resource (392 p.) 300 $aDescription based upon print version of record. 311 $a0-470-71549-9 320 $aIncludes bibliographical references and index. 327 $aThe 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 327 $a2 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 327 $a3 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 (?? > 0); 3.2.2 Case when the nontrivial fixed points exist (?? < 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 (? < 0); 3.4.1 Phase portraits; 3.4.2 Global bifurcation analysis 327 $a3.5 Global analysis for hardening nonlinear stiffness (? > 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 327 $a4.3.3 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-Poincare? 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 327 $a4.8 Elliptic homotopy methods 330 $aThe 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 606 $aDuffing equations 606 $aNonlinear oscillators$xMathematical models 615 0$aDuffing equations. 615 0$aNonlinear oscillators$xMathematical models. 676 $a515.35 676 $a515/.35 676 $a620.001515355 701 $aBrennan$b Michael J$g(Michael John),$f1956-$01762454 701 $aKovacic$b Ivana$f1972-$01762455 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910876869203321 996 $aThe Duffing equation$94202425 997 $aUNINA