Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:B4L-A

Session:

Number:474

A numerical study on parametric resonance of intrinsic localized modes in coupled cantilever arrays

Masayuki Kimura,  Yasuo Matsushita,  Takashi Hikihara,  

pp.474-477

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.474

PDF download (1.7MB)

In a coupled cantilever array modeled as a coupled ordinary differential equation, symmetric and antisymmetric intrinsic localized modes (ILMs) exist. The symmetric ILM is stable while the other is unstable under the regime in which the ratio in nonlinearities of inter-site and on-site potentials is less than the critical value at which the stability change occurs. This paper shows that a stable ILM loses its stability when the system is parametrically excited. If the amplitude of parametric excitation is large enough, the destabilized ILM wanders in the whole system. The parameter region where the instability occurs are numerically investigated and compared with that in the Mathieu equation. The similarity of the shape of the regions strongly suggests that the instability is caused by the parametric resonance.

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