一类多频激励相对转动非线性动力学模型的重正规化解

摘要

用摄动理论研究了一类多频激励下具有非线性弹性力和摩阻力的相对转动非线性动力学模型．探讨了各种组合频率之间的关系，给出了使多种类型共振同时发生的条件，并用重正规化方法得出了模型在各相应条件下解的渐近表达式．%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.