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Normal Modes and Localization in Nonlinear Systems |
| Alexander F. Vakakis (Univ. of Illinois ); Leonid I. Manevitch (Russian Academy of Sciences, Moscow); Yuri V. Mikhlin (Kharkov Polytechnic Univ., Ukraine); Valery N. Pilipchuk (Ukrainian State Chemical and Technical Univ., Ukraine); Alexandr A. Zevin (TRANSMAG Research Institute, Ukrainian Academy of Sciences) |
| 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.
Much of the material presented is completely new or appearing here for the first time in Western engineering literature—including numerous mathematical techniques for studying NNMs, their bifurcations, and the localization phenomena associated with them. The authors describe strongly nonlinear analytical methodologies that permit the analytical treatment of oscillators in strongly nonlinear regimes. They then demonstrate the application of these methodologies in numerous practical engineering and physics problems. Also presented is the method of nonsmooth temporal transformations, which enables analytic perturbation studies of strongly nonlinear oscillations, a new asymptotic methodology for analyzing standing solitary waves in some classes of nonlinear partial differential equations, and some new results on localized or nonlocalized oscillations of vibro-impact systems. | | |
