Theoretical Physics, Mechanical Engineering - General & Miscellaneous, Dynamics - General & Miscellaneous, Mechanical Physics - General & Miscellaneous

Normal Modes and Localization in Nonlinear Systems

Name: Normal Modes and Localization in Nonlinear Systems
Author: Vakakis, Alexander F.
ISBN: 9789048157150

by Vakakis, Alexander F.

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Overview

This book contains a collection of original papers on nonlinear normal modes and localization in dynamical systems from leading experts in the field. The reader will find new analytical and computational techniques for studying normal modes and localization phenomena in nonlinear discrete and continuous oscillators. In addition, examples are provided of applications of these concepts to diverse problems of engineering and applied mathematics, such as nonlinear control of micro-gyroscopes, dynamics of floating offshore platforms, buckling of imperfect continua, order reduction of nonlinear systems, dynamics of nonlinear vibration absorbers, spatial localization and pattern formation in extended systems, singular asymptotics and nonlinear modal interactions and energy pumping in coupled oscillators.

About the Author, Vakakis, Alexander F.

Alexander F. Vakakis is an associate professor in the Department of Mechanical and Industrial Engineering of the University of Illinois at Urbana-Champaign. His research interests include linear and nonlinear dynamics and vibrations, modal analysis, structural wave propagation, and bioengineering. He is an NSF Young Investigator Award recipient (1994), and his research is supported by federal and industrial grants. He received his PhD from the California Institute of Technology in 1990.

Leonid I. Manevitch is a professor in the Institute of Chemical Physics at the Russian Academy of Sciences, Moscow. He has published numerous papers and books on nonlinear dynamics and its applications. His current research interests center on nonlinear phenomena in molecular dynamics.

Yuri V. Mikhlin is a professor in the Department of Applied Mathematics at Kharkov's Polytechnic University in the Ukraine. He received his doctor of science degree from the Institute of Mechanical Problems at the Russian Academy of Sciences. His current research focuses on nonlinear oscillations of conservative and vibro-impact systems and on nonlinear solitary waves.

Valery N. Pilipchuk is a professor and Head of the Department of Applied Mathematics at the Ukrainian State Chemical and Technological University, Dnepropetrovsk, Ukraine. He received his two doctor of science degrees from the Institute of Mechanical Problems at the Russian Academy of Sciences in 1992. His research interests include nonlinear oscillations and waves and the theory of ordinary differential equations.

Alexandr A. Zevin is a researcher at the Transmag Research Institute at the Ukrainian Academy of Sciences,Dnepropetrovsk, Ukraine. He received his doctor of science degree from the Institute of Mechanical Problems at the Russian Academy of Sciences in 1989. His current research interests include the qualitative theory of nonlinear oscillations, and the theory of nonlinear ordinary differential equations.

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Editorials

Booknews

Takes a new approach to vibration analysis of nonlinear systems, focusing on nonlinear normal modes (NNMs) and nonlinear mode localization, and demonstrating 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. For physicists, vibration specialists, design engineers, and researchers studying nonlinear dynamics, as well as graduate students in applied mechanics and mechanical engineering. Much of the material appears for the first time in English. Annotation c. Book News, Inc., Portland, OR (booknews.com)

From The Critics

Nonlinear normal modes (NNMs) provide a framework for studying numerous problems in nonlinear dynamics, such as bifurcations that give rise to NNMs with no linear analogs; symmetry-breaking localized nonlinear periodic motions and nonlinear motion confinement; forced resonances and jump phenomena; NNM-based order-reduction schemes for discretizing the dynamics of continuous oscillators; and nonlinear system identification. This collection of 15 original papers covers such specific topics as model localization in dynamics and buckling of linear imperfect continuous structures; nonlinear modal analysis of structural systems using multi-mode invariant manifolds; transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators; and application of nonlinear normal mode analysis to the nonlinear and coupled dynamics of a floating offshore platform with damping. Also published as vol. 25, nos. 1-3, 2001. Annotation c. Book News, Inc., Portland, OR (booknews.com)