多自由度非线性振动系统多频振动的渐近解

对ｎ个自由度的非线性振动系统引和主与派生系统各主振型相对应的ｎ个振型广义质心坐标，使得求解关于ｎ个广义坐标的联立发方程组的问题归结为求解关于各振型广义质心坐标的ｎ个单自由振动形式的微分方程的问题。

Asymptotic Solution of Multi-Frequency Vibration for Systems in Multi-Degree of Freedom Nonlinear Vibration

Introduces n-mode generalized center-of-mass coordinetes corresponding respectively to each dominant mode of the system derived form a n degree-of-fredom nolilinear vibrational system.The problem of solving a set of differential equations of n generalized coordinates is thus reduced to that of solving n differntial equations having single degree of freedom of vibration for each mode of generalized center of mass coordinathes.The asymptotic solution of each of the genelized coordinates can be obtained by the development of multiplex Fourier series and solving a set of linear algebraic equations.An analysis on the single frequency vibration of multi-degree-offreedom nolilinear vibrational system is given and can be taken as a special case.