Chaotic Oscillations in Mechanical Systems PDF Download

Author: Tomasz Kapitaniak
Publisher: Manchester University Press
ISBN: 9780719033643
Category : Health & Fitness
Languages : en
Pages : 240

View

Book Description

Author: L G Khazin
Publisher: John Wiley & Sons
ISBN: 9780471935247
Category :
Languages : en
Pages : 232

View

Book Description
Mechanical systems may be considered as an example of nonlinear science, since the nonlinear effects can arise from a number of sources, such as geometric nonlinearities, nonlinear body forces, constitutive relations, kinematics or boundary conditions.

Author: Barbara Blazejczyk-Okolewska
Publisher: World Scientific
ISBN: 9789810237165
Category : Science
Languages : en
Pages : 194

View

Book Description
This book is devoted to the theory of chaotic oscillations in mechanical systems. Detailed descriptions of the basic types of nonlinearity ? impacts and dry friction ? are presented. The properties of such behavior are discussed, and the numerical and experimental results obtained by the authors are presented.The dynamic properties of systems described here can be useful in the proper design and use of mechanics where such behavior still creates problems.This book will be very useful for anyone with a fundamental knowledge of nonlinear mechanics who is beginning research in the field.

Author: Aleksandr L?vovich Fradkov
Publisher: World Scientific
ISBN: 9789810230692
Category : Science
Languages : en
Pages : 410

View

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: Polina S. Landa
Publisher: Springer Science & Business Media
ISBN: 3540452524
Category : Mathematics
Languages : en
Pages : 401

View

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: Juri I. Neimark
Publisher: Springer Science & Business Media
ISBN: 9401125961
Category : Mathematics
Languages : en
Pages : 510

View

Book Description
This volume is devoted to stochastic and chaotic oscillations in dissipative systems. Chapter 1 deals with mathematical models of deterministic, discrete and distributed dynamical systems. In Chapter 2, the two basic trends of order and chaos are considered. The next three chapters describe stochasticity transformers, amplifiers and generators, turbulence, and phase portraits of steady-state motions and their bifurcations. Chapter 6 treats the topics of stochastic and chaotic attractors, and this is followed by two chapters dealing with routes to chaos and the quantitative characteristics of stochastic and chaotic motions. Finally, Chapter 9, which comprises more than one-third of the book, presents examples of systems having chaotic and stochastic motions drawn from mechanical, physical, chemical and biological systems. The book concludes with a comprehensive bibliography. For mathematicians, physicists, chemists and biologists interested in stochastic and chaotic oscillations in dynamical systems.

Author: Jan Awrejcewicz
Publisher: World Scientific
ISBN: 9812384596
Category : Science
Languages : en
Pages : 564

View

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: Earl H. Dowell
Publisher:
ISBN:
Category : Chaotic behavior in systems
Languages : en
Pages : 5

View

Book Description
Work has focussed on the following topics using the buckled beam as prototypical generic system. The effect of higher modes on the response of the buckled beam initial condition maps and their interpretation Lyapunov exponents (nonlinear eigenvalues) as a predictor of chaos necessary and sufficient conditions for chaos to occur systems with both positive and negative linear stiffness systems with nonlinear damping a (buckled) beam-tube with an internal flowing fluid a survey paper summarizing much of our work Mechanical systems, Rotorcraft, Missiles, Buckled beam, Lyapunov exponents, Chaotic oscillations. a buckled beam under a constant as well as oscillating transverse load a curved beam (or plate) held (on one side) against a rigid surface the development of 'turbulence' in an aeroelastic system that is responding chaotically in many degrees of freedom and an experimental study of a simple prototypical system exhibiting sensitivity to initial conditions and chaos ...

Author: Nikolai Verichev
Publisher: Springer Nature
ISBN: 3030361039
Category : Science
Languages : en
Pages : 197

View

Book Description
This book develops analytical methods for studying the dynamical chaos, synchronization, and dynamics of structures in various models of coupled rotators. Rotators and their systems are defined in a cylindrical phase space, and, unlike oscillators, which are defined in Rn, they have a wider “range” of motion: There are vibrational and rotational types for cyclic variables, as well as their combinations (rotational-vibrational) if the number of cyclic variables is more than one. The specificity of rotator phase space poses serious challenges in terms of selecting methods for studying the dynamics of related systems. The book chiefly focuses on developing a modified form of the method of averaging, which can be used to study the dynamics of rotators. In general, the book uses the “language” of the qualitative theory of differential equations, point mappings, and the theory of bifurcations, which helps authors to obtain new results on dynamical chaos in systems with few degrees of freedom. In addition, a special section is devoted to the study and classification of dynamic structures that can occur in systems with a large number of interconnected objects, i.e. in lattices of rotators and/or oscillators. Given its scope and format, the book can be used both in lectures and courses on nonlinear dynamics, and in specialized courses on the development and operation of relevant systems that can be represented by a large number of various practical systems: interconnected grids of various mechanical systems, various types of networks including not only mechanical but also biological systems, etc.

Author: Bram De Kraker
Publisher: World Scientific
ISBN: 9814497908
Category : Technology & Engineering
Languages : en
Pages : 462

View

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.