Normal modes and localization in nonlinear systems. (English) Zbl 0917.93001

Vakakis, Alexander F.; Manevitch, Leonid I.; Mikhlin, Yuri V.; Pilipchuk, Valery N.; Zevin, Alexandr A.

Chichester: John Wiley & Sons. 568 p. (1996).

Publisher’s 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.

MSC:

70-02	Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
70K25	Free motions for nonlinear problems in mechanics
70K40	Forced motions for nonlinear problems in mechanics
70J10	Modal analysis in linear vibration theory
34-02	Research exposition (monographs, survey articles) pertaining to ordinary differential equations
34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C23	Bifurcation theory for ordinary differential equations

Keywords:

vibrations; oscillators; nonlinear normal mode; nonlinear localization; motion confinement; symmetries