The renormalization solution for a class of relative rotation nonlinear dynamic model with multi-frequency excitation

Abstract

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Using the perturbation theory, a class of relative rotation nonlinear dynamical model possessing nonlinear elastic force, friction force and multi-frequency excitation is investigated. The relations for the frequency syntheses are investigated, and the conditions under which multi-typical resonance happens at the same time are given. Using the renormalization method, the asymptotic expansions for the solutions of the model under corresponding conditions are obtained.