Bifurcation And Chaos In Nonsmooth Mechanical Systems

Author : Jan Awrejcewicz,Claude-Henri Lamarque
Publisher : World Scientific
Page : 564 pages
File Size : 49,9 Mb
Release : 2003
Category : Science
ISBN : 9789812384591

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Bifurcation and Chaos in Nonsmooth Mechanical Systems by Jan Awrejcewicz,Claude-Henri Lamarque Pdf

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 : Marian Wiercigroch,Bram de Kraker
Publisher : World Scientific
Page : 464 pages
File Size : 53,6 Mb
Release : 2000-04-28
Category : Science
ISBN : 9789814497909

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Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities by Marian Wiercigroch,Bram de Kraker Pdf

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. Contents:PreliminariesMathematical Models of Mechanical Systems with DiscontinuitiesTemporal and Spatial Discontinuity TransformationsExtensions of Cell Mapping for Discontinuous SystemsImpact OscillatorDynamics of Piecewise Linear OscillatorsQuenching of Self-Excited Vibrations by Impact DamperDynamic Phenomena in Gear BoxesRigorous Methods and Numerical Results for Dry Friction ProblemsForced Self-Excited Vibration with Dry FrictionStick–Slip and the Phase-Space ReconstructionMultidegree of Freedom Systems with Dry FrictionDynamic Instabilities in Spinning DisksImpacts and Dry FrictionNonlinear Dynamics of Orthogonal Metal CuttingDynamics of Ultrasonic Drilling of Hard Materials Readership: Mechanical engineers. keywords:Nonlinear Dynamics;Discontinuity;Mechanical System;Impacts;Dry Friction;Applications;Chaos “… this volume provides readers with an excellent treatment of such discontinuous systems and can be a good source of ideas to attack those systems effectively … one is immediately obliged to recognize that it is in fact a series of fifteen jewels, which one would hardly find in the relevant more mathematically oriented literature.” Mathematical Reviews

Author : Remco Leine,Henk Nijmeijer
Publisher : Springer
Page : 236 pages
File Size : 42,9 Mb
Release : 2014-03-12
Category : Mathematics
ISBN : 3642535798

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Dynamics and Bifurcations of Non-Smooth Mechanical Systems by Remco Leine,Henk Nijmeijer Pdf

This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Author : Remco I. Leine,Henk Nijmeijer
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 40,7 Mb
Release : 2013-03-19
Category : Mathematics
ISBN : 9783540443988

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Dynamics and Bifurcations of Non-Smooth Mechanical Systems by Remco I. Leine,Henk Nijmeijer Pdf

This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Author : Zhanybai T. Zhusubaliyev,Erik Mosekilde
Publisher : World Scientific
Page : 377 pages
File Size : 44,6 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812384201

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Bifurcations and Chaos in Piecewise-smooth Dynamical Systems by Zhanybai T. Zhusubaliyev,Erik Mosekilde Pdf

Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.

Author : Michal Fečkan
Publisher : Springer Science & Business Media
Page : 378 pages
File Size : 52,7 Mb
Release : 2011-05-30
Category : Science
ISBN : 9783642182693

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Bifurcation and Chaos in Discontinuous and Continuous Systems by Michal Fečkan Pdf

"Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along with precise and complete proofs together with concrete applications presented by many stimulating and illustrating examples. A broad variety of nonlinear problems are studied involving difference equations, ordinary and partial differential equations, differential equations with impulses, piecewise smooth differential equations, differential and difference inclusions, and differential equations on infinite lattices as well. This book is intended for mathematicians, physicists, theoretically inclined engineers and postgraduate students either studying oscillations of nonlinear mechanical systems or investigating vibrations of strings and beams, and electrical circuits by applying the modern theory of bifurcation methods in dynamical systems. Dr. Michal Fečkan is a Professor at the Department of Mathematical Analysis and Numerical Mathematics on the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovakia. He is working on nonlinear functional analysis, bifurcation theory and dynamical systems with applications to mechanics and vibrations.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 46,6 Mb
Release : 2024-06-13
Category : Electronic
ISBN : 9789814474641

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Smooth and Nonsmooth High Dimensional Chaos and the Melnikov-Type Methods by Anonim Pdf

Author : Anonim
Publisher : Elsevier
Page : 400 pages
File Size : 50,8 Mb
Release : 2006-06-30
Category : Science
ISBN : 0080462669

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Bifurcation and Chaos in Complex Systems by Anonim Pdf

The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth chapter studies bifurcations and chaos in time-varying, parametrically excited nonlinear dynamical systems. The fifth chapter presents bifurcation analyses of modal interactions in distributed, nonlinear, dynamical systems of circular thin von Karman plates. The theories, methods and results presented in this book are of great interest to scientists and engineers in a wide range of disciplines. This book can be adopted as references for mathematicians, scientists, engineers and graduate students conducting research in nonlinear dynamical systems. · New Views for Difficult Problems · Novel Ideas and Concepts · Hilbert's 16th Problem · Normal Forms in Polynomial Hamiltonian Systems · Grazing Flow in Non-smooth Dynamical Systems · Stochastic and Fuzzy Nonlinear Dynamical Systems · Fuzzy Bifurcation · Parametrical, Nonlinear Systems · Mode Interactions in nonlinear dynamical systems

Author : Jan Awrejcewicz
Publisher : Springer
Page : 614 pages
File Size : 54,5 Mb
Release : 2014-09-17
Category : Mathematics
ISBN : 9783319076591

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Ordinary Differential Equations and Mechanical Systems by Jan Awrejcewicz Pdf

This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization. Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition. The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.

Author : Jan Awrejcewicz,Yuriy Pyr'yev
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 44,6 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9780387096537

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Nonsmooth Dynamics of Contacting Thermoelastic Bodies by Jan Awrejcewicz,Yuriy Pyr'yev Pdf

This work is devoted to an intensive study in contact mechanics, treating the nonsmooth dynamics of contacting bodies. Mathematical modeling is illustrated and discussed in numerous examples of engineering objects working in different kinematic and dynamic environments. Topics covered in five self-contained chapters examine non-steady dynamic phenomena which are determined by key factors: i.e., heat conduction, thermal stresses, and the amount of wearing. New to this monograph is the importance of the inertia factor, which is considered on par with thermal stresses. Nonsmooth Dynamics of Contacting Thermoelastic Bodies is an engaging accessible practical reference for engineers (civil, mechanical, industrial) and researchers in theoretical and applied mechanics, applied mathematics, physicists, and graduate students.

Author : Vladimir Nikolov Damgov
Publisher : World Scientific
Page : 574 pages
File Size : 52,6 Mb
Release : 2004-11-22
Category : Science
ISBN : 9789814497732

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Nonlinear And Parametric Phenomena: Theory And Applications In Radiophysical And Mechanical Systems by Vladimir Nikolov Damgov Pdf

The book comprises a broad panorama of phenomena occurring in four major classes of radiophysical and mechanical systems — linear, nonlinear, parametric, and nonlinear-parametric. An analytical technique for the broad circle of issues under consideration is developed. It is presented in a user-friendly form, allowing its further direct application in research practices.Analytical methods are presented for investigating modulation-parametric and nonlinear systems, oscillating systems with periodic and almost periodic time-dependent parameters, effects of adaptive self-organization in coupled resonance systems and oscillating systems under the action of external forces, nonlinear with respect to the coordinates of excited systems.Of an interdisciplinary nature, this volume can serve as a handbook for developing lecture courses such as Fundamentals of Nonlinear Dynamics and Theory of Nonlinear Oscillations, Theory of Nonlinear Circuits and Systems, Fundamentals of Radiophysics and Electronics, Theory of Signals and Theoretical Radiophysics, Theoretical Mechanics and Electrodynamics.

Author : Hendrik Nijmeijer,Alejandro Rodriguez-Angeles
Publisher : World Scientific
Page : 219 pages
File Size : 46,9 Mb
Release : 2003
Category : Technology & Engineering
ISBN : 9789812386052

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Synchronization of Mechanical Systems by Hendrik Nijmeijer,Alejandro Rodriguez-Angeles Pdf

The main goal of this book is to prove analytically and validate experimentally that synchronization in multi-composed mechanical systems can be achieved in the case of partial knowledge of the state vector of the systems, i.e. when only positions are measured. For this purpose, synchronization schemes based on interconnections between the systems, feedback controllers and observers are proposed. Because mechanical systems include a large variety of systems, and since it is impossible to address all of them, the book focuses on robot manipulators. Nonetheless the ideas developed here can be extended to other mechanical systems, such as mobile robots, motors and generators.

Author : Wanda Szempli?ska-Stupnicka
Publisher : World Scientific
Page : 118 pages
File Size : 43,5 Mb
Release : 2003
Category : Business & Economics
ISBN : 9812564373

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Chaos Bifurcations and Fractals Around Us by Wanda Szempli?ska-Stupnicka Pdf

During the last twenty years, a large number of books on nonlinearchaotic dynamics in deterministic dynamical systems haveappeared. These academic tomes are intended for graduate students andrequire a deep knowledge of comprehensive, advanced mathematics.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 2024-06-13
Category : Electronic
ISBN : 9789814465731

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Bifurcations in Piecewise-Smooth Continuous Systems by Anonim Pdf

Author : Tian Ma,Shouhong Wang
Publisher : World Scientific
Page : 392 pages
File Size : 51,9 Mb
Release : 2005
Category : Science
ISBN : 9789812562876

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Bifurcation Theory and Applications by Tian Ma,Shouhong Wang Pdf

- Provides a comprehensive and intuitive review of existing bifurcation theories - New theories for bifurcations from eigenvalues with even multiplicity - General recipes for applications