LEADER 05224nam 2200685Ia 450 001 9910144743903321 005 20170810191428.0 010 $a1-281-76444-2 010 $a9786611764449 010 $a3-527-61786-8 010 $a3-527-61787-6 035 $a(CKB)1000000000377414 035 $a(EBL)481441 035 $a(OCoLC)262835392 035 $a(SSID)ssj0000212143 035 $a(PQKBManifestationID)11174865 035 $a(PQKBTitleCode)TC0000212143 035 $a(PQKBWorkID)10137350 035 $a(PQKB)10877667 035 $a(MiAaPQ)EBC481441 035 $a(MiAaPQ)EBC7076167 035 $a(Au-PeEL)EBL7076167 035 $a(EXLCZ)991000000000377414 100 $a19951019d1996 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aNormal modes and localization in nonlinear systems$b[electronic resource] /$fAlexander F. Vakakis ... [et al.] 210 $aNew York $cWiley$dc1996 215 $a1 online resource (570 p.) 225 1 $aWiley series in nonlinear science 300 $aDescription based upon print version of record. 311 $a0-471-13319-1 320 $aIncludes bibliographical references (p. 517-547) and index. 327 $aNORMAL 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, 327 $a3.2.1 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, 327 $aCHAPTER 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, 327 $a7.2 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, 327 $a8.2.2 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, 327 $a10.1.2 Numerical Computations, 330 $aThis landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves. 410 0$aWiley series in nonlinear science. 606 $aNonlinear systems 606 $aVibration 608 $aElectronic books. 615 0$aNonlinear systems. 615 0$aVibration. 676 $a003.75 676 $a531.32 676 $a531/.32 701 $aVakakis$b Alexander F.$f1961-$0884234 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144743903321 996 $aNormal modes and localization in nonlinear systems$91974508 997 $aUNINA