{"product_id":"the-duffing-equation-nonlinear-oscillators-and-their-behaviour-hardback-9780470715499","title":"The Duffing Equation; Nonlinear Oscillators and their Behaviour (Hardback) 9780470715499","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Duffing Equation\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eNonlinear Oscillators and their Behaviour\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eIvana Kovacic (Author), Michael J. Brennan (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470715499, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 25 March 2011\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e392 pages\u003cbr\u003e23.6 x 16.3 x 2.6 cm, 0.699 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"The book is a very well written and tightly edited exposition, not only of Duffing equations, but also of the general behavior of nonlinear oscillators. The book is likely to be of interest and use to students, engineers, and researchers in the ongoing studies of nonlinear phenomena. The book cites over 340 references.\" (Zentralblatt MATH, 2011)  \u003cp\u003e \u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003ci\u003eThe Duffing Equation: Nonlinear Oscillators and their Behaviour\u003c\/i\u003e 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.\u003cbr\u003e \u003cbr\u003e   \u003cp\u003e\u003ci\u003eThe Duffing Equation\u003c\/i\u003e 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.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eIncludes a chapter devoted to historical background on Georg Duffing and the equation that was named after him.\u003c\/li\u003e \u003cli\u003eIncludes a chapter solely devoted to practical examples of systems whose dynamic behaviour is described by the Duffing equation.\u003c\/li\u003e \u003cli\u003eContains a comprehensive treatment of the various forms of the Duffing equation.\u003c\/li\u003e \u003cli\u003eUses experimental, analytical and numerical methods as well as concepts of nonlinear dynamics to treat the physical systems in a unified way.\u003c\/li\u003e \u003c\/ul\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eList of Contributors.  \u003cp\u003ePreface.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Background: On Georg Duffing and the Duffing Equation\u003c\/b\u003e (\u003ci\u003eIvana Kovacic and Michael J. Brennan\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e1.1 Introduction.\u003c\/p\u003e \u003cp\u003e1.2 Historical perspective.\u003c\/p\u003e \u003cp\u003e1.3 A brief biography of Georg Duffing.\u003c\/p\u003e \u003cp\u003e1.4 The work of Georg Duffing.\u003c\/p\u003e \u003cp\u003e1.5 Contents of Duffing's book.\u003c\/p\u003e \u003cp\u003e1.6 Research inspired by Duffing’s work.\u003c\/p\u003e \u003cp\u003e1.7 Some other books on nonlinear dynamics.\u003c\/p\u003e \u003cp\u003e1.8 Overview of this book.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Examples of Physical Systems Described by the Duffing Equation\u003c\/b\u003e (\u003ci\u003eMichael J. Brennan and Ivana Kovacic\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e2.1 Introduction.\u003c\/p\u003e \u003cp\u003e2.2 Nonlinear stiffness.\u003c\/p\u003e \u003cp\u003e2.3 The pendulum.\u003c\/p\u003e \u003cp\u003e2.4 Example of geometrical nonlinearity.\u003c\/p\u003e \u003cp\u003e2.5 A system consisting of the pendulum and nonlinear stiffness.\u003c\/p\u003e \u003cp\u003e2.6 Snap-through mechanism.\u003c\/p\u003e \u003cp\u003e2.7 Nonlinear isolator.\u003c\/p\u003e \u003cp\u003e2.8 Large deflection of a beam with nonlinear stiffness.\u003c\/p\u003e \u003cp\u003e2.9 Beam with nonlinear stiffness due to inplane tension.\u003c\/p\u003e \u003cp\u003e2.10 Nonlinear cable vibrations.\u003c\/p\u003e \u003cp\u003e2.11 Nonlinear electrical circuit.\u003c\/p\u003e \u003cp\u003e2.12 Summary.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Free Vibration of a Duffing Oscillator with Viscous Damping\u003c\/b\u003e (\u003ci\u003eHiroshi Yabuno\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e3.1 Introduction.\u003c\/p\u003e \u003cp\u003e3.2 Fixed points and their stability.\u003c\/p\u003e \u003cp\u003e3.3 Local bifurcation analysis.\u003c\/p\u003e \u003cp\u003e3.4 Global analysis for softening nonlinear stiffness (γ\u0026lt; 0).\u003c\/p\u003e \u003cp\u003e3.5 Global analysis for hardening nonlinear stiffness (γ\u0026lt; 0).\u003c\/p\u003e \u003cp\u003e3.6 Summary.\u003c\/p\u003e \u003cp\u003eAcknowledgments.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Analysis Techniques for the Various Forms of the Duffing Equation\u003c\/b\u003e (\u003ci\u003eLivija Cveticanin\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e4.1 Introduction.\u003c\/p\u003e \u003cp\u003e4.2 Exact solution for free oscillations of the Duffing equation with cubic nonlinearity.\u003c\/p\u003e \u003cp\u003e4.3 The elliptic harmonic balance method.\u003c\/p\u003e \u003cp\u003e4.4 The elliptic Galerkin method.\u003c\/p\u003e \u003cp\u003e4.5 The straightforward expansion method.\u003c\/p\u003e \u003cp\u003e4.6 The elliptic Lindstedt–Poincaré method.\u003c\/p\u003e \u003cp\u003e4.7 Averaging methods.\u003c\/p\u003e \u003cp\u003e4.8 Elliptic homotopy methods.\u003c\/p\u003e \u003cp\u003e4.9 Summary.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eAppendix AI: Jacob elliptic function and elliptic integrals.\u003c\/p\u003e \u003cp\u003eAppendix 4AII: The best \u003ci\u003eL\u003c\/i\u003e\u003csub\u003e2\u003c\/sub\u003e norm approximation.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Forced Harmonic Vibration of a Duffing Oscillator with Linear Viscous Damping\u003c\/b\u003e (\u003ci\u003eTamas Kalmar-Nagy and Balakumar Balachandran\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e5.1 Introduction.\u003c\/p\u003e \u003cp\u003e5.2 Free and forced responses of the linear oscillator.\u003c\/p\u003e \u003cp\u003e5.3 Amplitude and phase responses of the Duffing oscillator.\u003c\/p\u003e \u003cp\u003e5.4 Periodic solutions, Poincare sections, and bifurcations.\u003c\/p\u003e \u003cp\u003e5.5 Global dynamics.\u003c\/p\u003e \u003cp\u003e5.6 Summary.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Forced Harmonic Vibration of a Duffing Oscillator with Different Damping Mechanisms\u003c\/b\u003e (\u003ci\u003eAsok Kumar Mallik\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e6.1 Introduction.\u003c\/p\u003e \u003cp\u003e6.2 Classification of nonlinear characteristics.\u003c\/p\u003e \u003cp\u003e6.3 Harmonically excited Duffing oscillator with generalised damping.\u003c\/p\u003e \u003cp\u003e6.4 Viscous damping.\u003c\/p\u003e \u003cp\u003e6.5 Nonlinear damping in a hardening system.\u003c\/p\u003e \u003cp\u003e6.6 Nonlinear damping in a softening system.\u003c\/p\u003e \u003cp\u003e6.7 Nonlinear damping in a double-well potential oscillator.\u003c\/p\u003e \u003cp\u003e6.8 Summary.\u003c\/p\u003e \u003cp\u003eAcknowledgments.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Forced Harmonic Vibration in a Duffing Oscillator with Negative Linear Stiffness and Linear Viscous Damping\u003c\/b\u003e (\u003ci\u003eStefano Lenci and Giuseppe Rega\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e7.1 Introduction.\u003c\/p\u003e \u003cp\u003e7.2 Literature survey.\u003c\/p\u003e \u003cp\u003e7.3 Dynamics of conservative and nonconservative systems.\u003c\/p\u003e \u003cp\u003e7.4 Nonlinear periodic oscillations.\u003c\/p\u003e \u003cp\u003e7.5 Transition to complex response.\u003c\/p\u003e \u003cp\u003e7.6 Nonclassical analyses.\u003c\/p\u003e \u003cp\u003e7.7 Summary.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Forced Harmonic Vibration of an Asymmetric Duffing Oscillator\u003c\/b\u003e (\u003ci\u003eIvana Kovacic and Michael J. Brennan\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e8.1 Introduction.\u003c\/p\u003e \u003cp\u003e8.2 Models of the systems under consideration.\u003c\/p\u003e \u003cp\u003e8.3 Regular response of the pure cubic oscillator.\u003c\/p\u003e \u003cp\u003e8.4 Regular response of the single-well Helmholtz–Duffing oscillator.\u003c\/p\u003e \u003cp\u003e8.5 Chaotic response of the pure cubic oscillator.\u003c\/p\u003e \u003cp\u003e8.6 Chaotic response of the single-well Helmholtz–Duffing oscillator.\u003c\/p\u003e \u003cp\u003e8.7 Summary.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix Translation of Sections from Duffing's Original Book\u003c\/b\u003e (\u003ci\u003eKeith Worden and Heather Worden\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e\u003cb\u003eGlossary.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex.\u003c\/b\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mechanical engineering \u0026amp; materials [\u003ca title=\"See our other books on Mechanical engineering \u0026amp; materials\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mechanical%20engineering%20\u0026amp;%20materials%20%5BTG%5D%22\"\u003eTG\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52278024077592,"sku":"9780470715499","price":94.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470715499.jpg?v=1781456113","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-duffing-equation-nonlinear-oscillators-and-their-behaviour-hardback-9780470715499","provider":"Freshly Printed Books","version":"1.0","type":"link"}