Vibration Of Strongly Nonlinear Discontinuous Systems

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Vibration Of Strongly Nonlinear Discontinuous Systems

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Author : V.I. Babitsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-08-10

Vibration Of Strongly Nonlinear Discontinuous Systems written by V.I. Babitsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-10 with Computers categories.

This monograph addresses the systematic representation of the methods of analysis developed by the authors as applied to such systems. Particular features of dynamic processes in such systems are studied. Special attention is given to an analysis of different resonant phenomena taking unusual and diverse forms.

Vibration Of Strongly Nonlinear Discontinuous Systems

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Author : V.I. Babitsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-02

Vibration Of Strongly Nonlinear Discontinuous Systems written by V.I. Babitsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-02 with Technology & Engineering categories.

Among the wide diversity of nonlinear mechanical systems, it is possible to distinguish a representative class of the systems which may be characterised by the presence of threshold nonlinear positional forces. Under particular configurations, such systems demonstrate a sudden change in the behaviour of elastic and dissipative forces. Mathematical study of such systems involves an analysis of equations of motion containing large-factored nonlinear terms which are associated with the above threshold nonlinearity. Due to this, we distinguish such discontinuous systems from the much wider class of essentially nonlinear systems, and define them as strongly nonlinear systems'. The vibration occurring in strongly nonlinear systems may be characterised by a sudden and abrupt change of the velocity at particular time instants. Such a vibration is said to be non-smooth. The systems most studied from this class are those with relaxation (Van Der Pol, Andronov, Vitt, Khaikhin, Teodorchik, etc. [5,65,70,71,98,171,181]), where the non-smooth vibration usually appears due to the presence of large nonconservative nonlinear forces. Equations of motion describing the vibration with relaxation may be written in such a manner that the highest derivative is accompanied by a small parameter. The methods of integration of these equations have been developed by Vasilieva and Butuzov [182], Volosov and Morgunov [190], Dorodnitsin [38], Zheleztsov [201], Mischenko and Rozov [115], Pontriagin [137], Tichonov [174,175], etc. In a system with threshold nonlinearity, the non-smooth vibration occurs due to the action of large conservative forces. This is distinct from a system with relaxation.

Non Smooth Deterministic Or Stochastic Discrete Dynamical Systems

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Author : Jerome Bastien
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-18

Non Smooth Deterministic Or Stochastic Discrete Dynamical Systems written by Jerome Bastien and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-18 with Mathematics categories.

This book contains theoretical and application-oriented methods to treat models of dynamical systems involving non-smooth nonlinearities. The theoretical approach that has been retained and underlined in this work is associated with differential inclusions of mainly finite dimensional dynamical systems and the introduction of maximal monotone operators (graphs) in order to describe models of impact or friction. The authors of this book master the mathematical, numerical and modeling tools in a particular way so that they can propose all aspects of the approach, in both a deterministic and stochastic context, in order to describe real stresses exerted on physical systems. Such tools are very powerful for providing reference numerical approximations of the models. Such an approach is still not very popular nevertheless, even though it could be very useful for many models of numerous fields (e.g. mechanics, vibrations, etc.). This book is especially suited for people both in research and industry interested in the modeling and numerical simulation of discrete mechanical systems with friction or impact phenomena occurring in the presence of classical (linear elastic) or non-classical constitutive laws (delay, memory effects, etc.). It aims to close the gap between highly specialized mathematical literature and engineering applications, as well as to also give tools in the framework of non-smooth stochastic differential systems: thus, applications involving stochastic excitations (earthquakes, road surfaces, wind models etc.) are considered. Contents 1. Some Simple Examples. 2. Theoretical Deterministic Context. 3. Stochastic Theoretical Context. 4. Riemannian Theoretical Context. 5. Systems with Friction. 6. Impact Systems. 7. Applications–Extensions. About the Authors Jérôme Bastien is Assistant Professor at the University Lyon 1 (Centre de recherche et d'Innovation sur le sport) in France. Frédéric Bernardin is a Research Engineer at Département Laboratoire de Clermont-Ferrand (DLCF), Centre d'Etudes Techniques de l'Equipement (CETE), Lyon, France. Claude-Henri Lamarque is Head of Laboratoire Géomatériaux et Génie Civil (LGCB) and Professor at Ecole des Travaux Publics de l'Etat (ENTPE), Vaulx-en-Velin, France.

A Smooth And Discontinuous Oscillator

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Author : Qingjie Cao
language : en
Publisher: Springer
Release Date : 2016-09-27

A Smooth And Discontinuous Oscillator written by Qingjie Cao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-27 with Technology & Engineering categories.

This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

Nonlinear Dynamics Volume 1

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Author : Gaetan Kerschen
language : en
Publisher: Springer
Release Date : 2016-04-22

Nonlinear Dynamics Volume 1 written by Gaetan Kerschen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-22 with Technology & Engineering categories.

Nonlinear Dynamics, Volume 1. Proceedings of the 34th IMAC, A Conference and Exposition on Dynamics of Multiphysical Systems: From Active Materials to Vibroacoustics, 2016, the fi rst volume of ten from the Conference, brings together contributions to this important area of research and engineering. Th e collection presents early fi ndings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: • Nonlinear Oscillations • Nonlinear Modal Analysis • Nonlinear System Identifi cation • Nonlinear Modeling & Simulation • Nonlinearity in Practice • Nonlinearity in Multi-Physics Systems • Nonlinear Modes and Modal Interactions

Hilbert Transform Applications In Mechanical Vibration

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Author : Michael Feldman
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-08

Hilbert Transform Applications In Mechanical Vibration written by Michael Feldman and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-08 with Science categories.

Hilbert Transform Applications in Mechanical Vibration addresses recent advances in theory and applications of the Hilbert transform to vibration engineering, enabling laboratory dynamic tests to be performed more rapidly and accurately. The author integrates important pioneering developments in signal processing and mathematical models with typical properties of mechanical dynamic constructions such as resonance, nonlinear stiffness and damping. A comprehensive account of the main applications is provided, covering dynamic testing and the extraction of the modal parameters of nonlinear vibration systems, including the initial elastic and damping force characteristics. This unique merger of technical properties and digital signal processing allows the instant solution of a variety of engineering problems and the in-depth exploration of the physics of vibration by analysis, identification and simulation. This book will appeal to both professionals and students working in mechanical, aerospace, and civil engineering, as well as naval architecture, biomechanics, robotics, and mechatronics. Hilbert Transform Applications in Mechanical Vibration employs modern applications of the Hilbert transform time domain methods including: The Hilbert Vibration Decomposition method for adaptive separation of a multi-component non-stationary vibration signal into simple quasi-harmonic components; this method is characterized by high frequency resolution, which provides a comprehensive account of the case of amplitude and frequency modulated vibration analysis. The FREEVIB and FORCEVIB main applications, covering dynamic testing and extraction of the modal parameters of nonlinear vibration systems including the initial elastic and damping force characteristics under free and forced vibration regimes. Identification methods contribute to efficient and accurate testing of vibration systems, avoiding effort-consuming measurement and analysis. Precise identification of nonlinear and asymmetric systems considering high frequency harmonics on the base of the congruent envelope and congruent frequency. Accompanied by a website at www.wiley.com/go/feldman, housing MATLAB®/ SIMULINK codes.

Tractable Models Of Solid Mechanics

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Author : Oleg V. Gendelman
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-04

Tractable Models Of Solid Mechanics written by Oleg V. Gendelman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-04 with Technology & Engineering categories.

This book describes significant tractable models used in solid mechanics - classical models used in modern mechanics as well as new ones. The models are selected to illustrate the main ideas which allow scientists to describe complicated effects in a simple manner and to clarify basic notations of solid mechanics. A model is considered to be tractable if it is based on clear physical assumptions which allow the selection of significant effects and relatively simple mathematical formulations. The first part of the book briefly reviews classical tractable models for a simple description of complex effects developed from the 18th to the 20th century and widely used in modern mechanics. The second part describes systematically the new tractable models used today for the treatment of increasingly complex mechanical objects – from systems with two degrees of freedom to three-dimensional continuous objects.

Discontinuous Dynamical Systems On Time Varying Domains

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Author : Albert C. J. Luo
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-06

Discontinuous Dynamical Systems On Time Varying Domains written by Albert C. J. Luo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-06 with Science categories.

"Discontinuous Dynamical Systems on Time-varying Domains" is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time-invariant domains, this book presents discontinuous dynamical systems on time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed. From such a theory, principles of dynamical system interactions without any physical connections are presented. Several discontinuous systems on time-varying domains are analyzed in detail to show how to apply the theory to practical problems. The book can serve as a reference book for researchers, advanced undergraduate and graduate students in mathematics, physics and mechanics. Dr. Albert C. J. Luo is a professor at Southern Illinois University Edwardsville, USA. His research is involved in the nonlinear theory of dynamical systems. His main contributions are in the following aspects: a stochastic and resonant layer theory in nonlinear Hamiltonian systems, singularity on discontinuous dynamical systems, and approximate nonlinear theories for a deformable-body.

Nonlinear Dynamics

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Author : Valery N. Pilipchuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-09

Nonlinear Dynamics written by Valery N. Pilipchuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-09 with Science categories.

Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of “unusual” physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of Nonlinear Dynamics appeared to be very diverse, individual and technically complicated. This book makes an attempt to find a common ground for nonlinear dynamic analyses based on the existence of strongly nonlinear but quite simple counterparts to the linear models and tools. It is shown that, since the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, then translations and reflections, impact oscillators, and hyperbolic (Clifford’s) algebras must give rise to some “quasi impact” methodology. Such strongly nonlinear methods are developed in several chapters of this book based on the idea of non-smooth time substitutions. Although most of the illustrations are based on mechanical oscillators, the area of applications may include also electric, electro-mechanical, electrochemical and other physical models generating strongly anharmonic temporal signals or spatial distributions. Possible applications to periodic elastic structures with non-smooth or discontinuous characteristics are outlined in the final chapter of the book.

Nonlinear Targeted Energy Transfer In Mechanical And Structural Systems

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Author : Alexander F. Vakakis
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-24

Nonlinear Targeted Energy Transfer In Mechanical And Structural Systems written by Alexander F. Vakakis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-24 with Technology & Engineering categories.

This monograph evolved over a period of nine years from a series of papers and presentations addressing the subject of passive vibration control of mechanical s- tems subjected to broadband, transient inputs. The unifying theme is Targeted - ergy Transfer – TET, which represents a new and unique approach to the passive control problem, in which a strongly nonlinear, fully passive, local attachment, the Nonlinear Energy Sink – NES, is employed to drastically alter the dynamics of the primary system to which it is attached. The intrinsic capacity of the properly - signed NES to promote rapid localization of externally applied (narrowband) - bration or (broadband) shock energy to itself, where it can be captured and dis- pated, provides a powerful strategy for vibration control and the opens the pos- bility for a wide range of applications of TET, such as, vibration and shock i- lation, passive energy harvesting, aeroelastic instability (?utter) suppression, se- mic mitigation, vortex shedding control, enhanced reliability designs (for ex- ple in power grids) and others. The monograph is intended to provide a thorough explanation of the analytical, computational and experimental methods needed to formulate and study TET in mechanical and structural systems. Several prac- cal engineering applications are examined in detail, and experimental veri?cation and validation of the theoretical predictions are provided as well. The authors also suggest a number of possible future applications where application of TET seems promising. The authors are indebted to a number of sponsoring agencies.