Normal modes and localization in nonlinear systems - Info and Reading Options

The Open Library:

Vibration analysis of nonlinear systems poses great challenges in both physics and engineering. This innovative book takes a completely new approach to the subject, focusing on nonlinear normal modes (NNMs) and nonlinear mode localization, and demonstrates that these concepts provide an excellent analytical tool for the study of nonlinear phenomena that cannot be analyzed by conventional techniques based on linear or quasi-linear theory. Written by professor Alexander F. Vakakis and four colleagues from Russia and the Ukraine, the book employs the similarity of NNMs to the normal modes of classical vibration theory to create a new perspective on this highly specialized, yet steadily growing field. Providing a solid foundation in theory, the authors explain, for example, the design of systems with passive or active motion confinement properties and examine applications of essentially nonlinear phenomena to the vibration and shock isolation of flexible, large-scale structures.

Open Data:

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 NNMs -- 5.1 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

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