05224nam 2200685Ia 450 991014474390332120170810191428.01-281-76444-297866117644493-527-61786-83-527-61787-6(CKB)1000000000377414(EBL)481441(OCoLC)262835392(SSID)ssj0000212143(PQKBManifestationID)11174865(PQKBTitleCode)TC0000212143(PQKBWorkID)10137350(PQKB)10877667(MiAaPQ)EBC481441(MiAaPQ)EBC7076167(Au-PeEL)EBL7076167(EXLCZ)99100000000037741419951019d1996 uy 0engur|n|---|||||txtccrNormal modes and localization in nonlinear systems[electronic resource] /Alexander F. Vakakis ... [et al.]New York Wileyc19961 online resource (570 p.)Wiley series in nonlinear scienceDescription based upon print version of record.0-471-13319-1 Includes bibliographical references (p. 517-547) and index.NORMAL MODES AND LOCALIZATION IN NONLINEAR SYSTEMS; CONTENTS; Preface; Acknowledgments; CHAPTER 1 Introduction; 1.1 Concepts of Nonlinear Normal Mode (NNM) and Nonlinear Localization,; 1.2 Example: NNMs of a Two-DOF Dynamical System,; CHAPTER 2 NNMs in Discrete Oscillators: Qualitative Results; 2.1 Preliminary Formulation,; 2.2 Existence Theorem for NNMs,; 2.3 Applications of the Existence Theorem,; 2.4 NNMs in Systems with Concave and Convex Nonlinearities,; CHAPTER 3 NNMs in Discrete Oscillators: Quantitative Results; 3.1 Introduction,; 3.2 Conservative Systems,3.2.1 Trajectories of NNMs in Configuration Space,3.2.2 Similar NNMs,; 3.2.3 Nonsimilar NNMs and Matched Asymptotic Expansions,; 3.2.4 Application to a Two-DOF Strongly Nonlinear System,; 3.3 Invariant Manifold Approaches for NNMs,; 3.4 Analysis of NNMs Using Group Theory,; 3.5 Vibro-Impact Systems,; CHAPTER 4 Stability and Bifurcations of NNMs; 4.1 General Stability Results,; 4.2 Similar NNMs,; 4.2.1 Analysis of Stability Boundaries,; 4.2.2 Finite-Zoning Instability Conditions,; 4.3 Nonsimilar NNMs,; 4.4 NNM Bifurcations in a System in Internal Resonance,; 4.5 Stability of Stationary Waves,CHAPTER 5 Resonances of Discrete Systems Close to NNMs5.1 Exact Steady State Motions,; 5.2 Admissible Forcing Functions for Steady State Motions,; 5.3 Effects of NNM Bifurcations on the Resonances,; CHAPTER 6 The Method of Nonsmooth Temporal Transformations ( NSTTs); 6.1 Preliminaries,; 6.2 Representations of Functions Using NSTTs,; 6.3 Analysis of Dynamical Systems,; CHAPTER 7 Nonlinear Localization in Discrete Systems; 7.1 Weakly Coupled Oscillators: Qualitative Results,; 7.1.1 Existence and Stability of Periodic Solutions,; 7.1.2 Nonlinear Mode Localization,7.2 Mode Localization in Systems with Cyclic Symmetry,7.2.1 Asymptotic Analysis of Modal Curves,; 7.2.2 Transition from Localization to Nonlocalization,; 7.3 Mode Localization in a Strongly Nonlinear System,; 7.4 Localization in Impulsively Forced Systems,; CHAPTER 8 NNMs in Continuous Systems; 8.1 Systems of Finite Spatial Extent,; 8.1.1 Direct Analysis of the Equations of Motion,; 8.1.2 Analysis by Discretization,; 8.1.3 Stability Analysis of NNMs,; 8.2 Systems of Infinite Spatial Extent,; 8.2.1 Stationary Waves as NNMs,8.2.2 Waves in Attenuation Zones of Monocoupled Nonlinear Periodic Systems,CHAPTER 9 Nonlinear Localization in Systems of Coupled Beams; 9.1 Theoretical Analysis,; 9.1.1 Nonlinear Mode Localization: Discretization,; 9.1.2 Passive Motion Confinement of Impulsive Responses,; 9.1.3 Nonlinear Localization of Forced Steady-State Motions,; 9.1.4 Nonlinear Mode Localization: Direct Analysis of the Equations of Motion,; 9.2 Experimental Verification,; CHAPTER 10 Nonlinear Localization in Other Continuous Systems; 10.1 Multispan Nonlinear Beams,; 10.1.1 Derivation of the Modulation Equations,10.1.2 Numerical Computations,This landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves.Wiley series in nonlinear science.Nonlinear systemsVibrationElectronic books.Nonlinear systems.Vibration.003.75531.32531/.32Vakakis Alexander F.1961-884234MiAaPQMiAaPQMiAaPQBOOK9910144743903321Normal modes and localization in nonlinear systems1974508UNINA