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Mechanics of Nonlinear Systems with Internal Resonances

Mechanics of Nonlinear Systems with Internal Resonances

by Manevitch, Leonid
No customer reviews yet ISBN 9781860945106

One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied.

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Pub dateMay 13, 2005
ISBN-101860945104
ISBN-139781860945106
LanguageEnglish
Last updated 2026-03-13 13:28
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