Normal Modes and Localization in Nonlinear Systems
Wiley Series in Nonlinear Science
1. Edition July 1996
552 Pages, Hardcover
Monograph
Short Description
This book is devoted to the study of vibrations of discrete and continuous nonlinear oscillators. Its unique approach is based on the concept of nonlinear normal mode (NNM). This concept provides an excellent framework for understanding and analyzing free and forced oscillations of mechanical systems, predicting bifurcations of solutions, and understanding a variety of essentially nonlinear phenomena, such as nonlinear localization and motion confinement in systems with symmetries.
- Out of print -
Further versions
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.
NNMs in Discrete Oscillators: Quantitative Results.
Stability and Bifurcations of NNMs.
Resonances of Discrete Systems Close to NNMs.
The Method of Nonsmooth Temporal Transformations (NSTTs).
Nonlinear Localization in Discrete Systems.
NNMs in Continuous Systems.
Nonlinear Localization in Systems of Coupled Beams.
Nonlinear Localization in Other Continuous Systems.
References.
Index.
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.
