Coupled nonlinear oscillators: metamorphoses of amplitude profiles. The case of the approximate effective equation

Details Coupled nonlinear oscillators: metamorphoses of amplitude profiles. The case of the approximate effective equation Coupled nonlinear oscillators: metamorphoses of amplitude profiles. The case of the approximate effective equation

2010-12-09

arxiv.org/abs/1012.2140v1

Acta Physica Polonica B 42 (10), 2011, 2063-2076

Nonlinear Sciences

Chaotic Dynamics

13 pages, 9 figures

Scientific paper

10.5506/APhysPolB.42.2063

We study dynamics of two coupled periodically driven oscillators. Important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation are determined within the Krylov-Bogoliubov-Mitropolsky approach to get the amplitude profiles $AOmega) $. Dependence of the amplitude $A$ of nonlinear resonances on the frequency $ \Omega $ is much more complicated than in the case of one Duffing oscillator and hence new nonlinear phenomena are possible. In the present paper we study metamorphoses of the function $A(\Omega) $ induced by changes of the control parameters.

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