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Triple scale analysis of periodic solutions and resonance of some asymmetric non linear vibrating systems. (English) Zbl 1304.34101

A paper a triple scale analysis of small periodic solutions of free vibrations of a discrete structure without damping and with local smooth nonlinearity is considered. After this, a similar system and a periodic forcing in a resonance situation is considered too. The use of double or triple scale expansion is compared. The authors emphasizes that the use of three times scales, instead of two times scales presented in a preliminary work (by the same authors), provides a much improved insight in the behaviour of the forces response close to resonance. The amplitude of the response with respect to the frequency forcing is described and it is related to the frequency of a free periodic vibrations.

MSC:

34E13 Multiple scale methods for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
70K30 Nonlinear resonances for nonlinear problems in mechanics
34E05 Asymptotic expansions of solutions to ordinary differential equations
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