Chaotic Mechanics in Systems with Impacts and Friction


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.




Applied Nonlinear Dynamics And Chaos Of Mechanical Systems With Discontinuities


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.




Bifurcation and Chaos in Nonsmooth Mechanical Systems


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.







Selected Topics in Vibrational Mechanics


Book Description

Vibrational mechanics is a new, intensively developing section of nonlinear dynamics and of the theory of nonlinear oscillations. It presents a general approach to the study of the effects of vibration on nonlinear systems. This approach is characterized by simplicity of application and by physical clearness. In recent years a number of new, essential results have been obtained both on the development of the mathematical apparatus of vibrational mechanics and on the solution of certain applied problems. This book reflects those results through the ingenious presentation of the authors -- well-known scientists from Germany, Denmark and Russia. For the convenience of readers, the main content is preceded by a brief description of the main theses of vibrational mechanics.




Bifurcation And Chaos In Nonsmooth Mechanical Systems


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.




Control of Homoclinic Chaos by Weak Periodic Perturbations


Book Description

This monograph presents a reasonably rigorous theory of a highly relevant chaos control method: suppression?enhancement of chaos by weak periodic excitations in low-dimensional, dissipative and non-autonomous systems. The theory provides analytical estimates of the ranges of parameters of the chaos-controlling excitation for suppression?enhancement of the initial chaos.The important applications of the theory presented in the book include: (1) control of chaotic escape from a potential well; (2) suppression of chaos in a driven Josephson junction; (3) control of chaotic solitons in Frenkel?Kontorova chains; (4) control of chaotic breather dynamics in perturbed sine-Gordon equations; (5) control of chaotic charged particles in electrostatic wave packets.




Chaos for Engineers


Book Description

A desription of the new mathematical ideas in nonlinear dynamics in such a way that engineers can apply them to real physical systems.




Damage Prognosis


Book Description

Damage prognosis is a natural extension of damage detection and structural health monitoring and is forming a growing part of many businesses. This comprehensive volume presents a series of fundamental topics that define the new area of damage prognosis. Bringing together essential information in each of the basic technologies necessary to perform damage prognosis, it also reflects the highly interdisciplinary nature of the industry through the extensive referencing of each of the component disciplines. Taken from lectures given at the Pan American Advanced Studies Institute in Damage Prognosis sponsored by the US National Science Foundation in cooperation with Los Alamos National Laboratories, this book will be essential reading for anyone looking to get to grips with the fundamentals of damage prognosis. Presents the 'ground rules' for Damage Prognosis. Deals with interdisciplinary topics: rotating machines, aerospace structures, automotive components and civil structures. Covers essential technical material: equations, graphs and plots, tables and photographs. Offers additional material from the associated workshop on an active web site.




Cellular Neural Networks, Multi-scroll Chaos and Synchronization


Book Description

For engineering applications that are based on nonlinear phenomena, novel information processing systems require new methodologies and design principles. This perspective is the basis of the three cornerstones of this book: cellular neural networks, chaos and synchronization. Cellular neural networks and their universal machine implementations offer a well-established platform for processing spatial-temporal patterns and wave computing. Multi-scroll circuits are generalizations to the original Chua's circuit, leading to chip implementable circuits with increasingly complex attractors. Several applications make use of synchronization techniques for nonlinear systems. A systematic overview is given for Lur'e representable systems with global synchronization criteria for master-slave and mutual synchronization, robust synchronization, HV synchronization, time-delayed systems and impulsive synchronization.