Chaotic Oscillations in Mechanical Systems PDF Download
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Author: Tomasz Kapitaniak
Publisher: Manchester University Press
ISBN: 9780719033643
Category : Health & Fitness
Languages : en
Pages : 240
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Book Description
Author: Tomasz Kapitaniak
Publisher: Manchester University Press
ISBN: 9780719033643
Category : Health & Fitness
Languages : en
Pages : 240
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Book Description
Author: Bram De Kraker
Publisher: World Scientific
ISBN: 9814497908
Category : Technology & Engineering
Languages : en
Pages : 462
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Book Description
Rapid developments in nonlinear dynamics and chaos theory have led to publication of many valuable monographs and books. However, most of these texts are devoted to the classical nonlinear dynamics systems, for example the Duffing or van der Pol oscillators, and either neglect or refer only briefly to systems with motion-dependent discontinuities. In engineering practice a good part of problems is discontinuous in nature, due to either deliberate reasons such as the introduction of working clearance, and/or the finite accuracy of the manufacturing processes.The main objective of this volume is to provide a general methodology for describing, solving and analysing discontinuous systems. It is compiled from the dedicated contributions written by experts in the field of applied nonlinear dynamics and chaos.The main focus is on mechanical engineering problems where clearances, piecewise stiffness, intermittent contact, variable friction or other forms of discontinuity occur. Practical applications include vibration absorbers, percussive drilling of hard materials and dynamics of metal cutting.
Author: Polina S. Landa
Publisher: Springer Science & Business Media
ISBN: 9783540410010
Category : Mathematics
Languages : en
Pages : 424
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Book Description
This text maps out the modern theory of non-linear oscillations. The material is presented in a non-traditional manner and emphasises the new results of the theory - obtained partially by the author, who is one of the leading experts in the area. Among the topics are: synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration on modification of characteristics and behaviour of the non-linear systems.
Author: Alexander L Fradkov
Publisher: World Scientific
ISBN: 9814497665
Category : Technology & Engineering
Languages : en
Pages : 407
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Book Description
This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.
Author: Jan Awrejcewicz
Publisher: World Scientific
ISBN: 9812384596
Category : Science
Languages : en
Pages : 564
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Book Description
This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.
Author: John Guckenheimer
Publisher: Springer Science & Business Media
ISBN: 1461211409
Category : Mathematics
Languages : en
Pages : 475
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Book Description
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532
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Book Description
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Author: Jan Awrejcewicz
Publisher: World Scientific
ISBN: 9789812564801
Category : Mathematics
Languages : en
Pages : 566
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Book Description
This book presents the theoretical frame for studying lumped nonsmoothdynamical systems: the mathematical methods are recalled, and adaptednumerical methods are introduced (differential inclusions, maximalmonotone operators, Filippov theory, Aizerman theory, etc.
Author: Guanrong Chen
Publisher: World Scientific
ISBN: 9814488704
Category : Technology & Engineering
Languages : en
Pages : 656
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Book Description
In this volume, leading experts present current achievements in the forefront of research in the challenging field of chaos in circuits and systems, with emphasis on engineering perspectives, methodologies, circuitry design techniques, and potential applications of chaos and bifurcation. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this field. It is suitable for readers ranging from graduate students, university professors, laboratory researchers and industrial practitioners to applied mathematicians and physicists in electrical, electronic, mechanical, physical, chemical and biomedical engineering and science.
Author: Giuseppe Rega
Publisher: Springer Science & Business Media
ISBN: 9781402032677
Category : Technology & Engineering
Languages : en
Pages : 544
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Book Description
The interest of the applied mechanics community in chaotic dynamics of engineering systems has exploded in the last fifteen years, although research activity on nonlinear dynamical problems in mechanics started well before the end of the Eighties. It developed first within the general context of the classical theory of nonlinear oscillations, or nonlinear vibrations, and of the relevant engineering applications. This was an extremely fertile field in terms of formulation of mechanical and mathematical models, of development of powerful analytical techniques, and of understanding of a number of basic nonlinear phenomena. At about the same time, meaningful theoretical results highlighting new solution methods and new or complex phenomena in the dynamics of deterministic systems were obtained within dynamical systems theory by means of sophisticated geometrical and computational techniques. In recent years, careful experimental studies have been made to establish the actual occurrence and observability of the predicted dynamic phenomena, as it is vitally needed in all engineering fields. Complex dynamics have been shown to characterize the behaviour of a great number of nonlinear mechanical systems, ranging from aerospace engineering applications to naval applications, mechanical engineering, structural engineering, robotics and biomechanics, and other areas. The International Union of Theoretical and Applied Mechanics grasped the importance of such complex phenomena in the Eighties, when the first IUTAM Symposium devoted to the general topic of nonlinear and chaotic dynamics in applied mechanics and engineering was held in Stuttgart (1989).
