阻尼振动系统的强迫响应

本文讨论阻尼振动系统(离散或连续系统)在周期外激励作用下的强迫响应;系统的阻尼阵不能对角化.导出了强迫响应一般解的显式解析表达式.利用这些解式,本文对某些振动现象作了较普遍的解析讨论.如,从一般角度讨论了单阻尼振动系统特有的“固定振幅点”现象;讨论了同相位外激励作用下产生同相位响应的条件等等.本文导出的解式对一大类系统仅含很低阶的矩阵求逆运算,因而在计算机数值计算上.本方法比之于现有方法,具有程序简单、耗时少和精度高等优点.本方法可平行应用于转子动力学的不平衡响应分析.

The Forced Response of the Damping Dynamic Systems

This paper deals with the forced harmonie responses of the discrete or continuous damped systems to harmonic excitation, where the viscous damping matrix cannot be diagonalized. The explicit expressions of the response solutions are given. Hence, with these expressions, some general and analytical study of some phenomena in vibration is made. For example, the "fixed amplitude point" phenomena in the single damped systems have been demonstrated generally. The conditions, under which all forces that exert on the system and possess common phase, which will excite common phase responses, are also discussed.The solutions deduced here only involve the inverse matrices of lower order. Thus, in the numerical computation for digital computers, the method is more simple, economical, and accurate than others.The method described here can be used in the analysis of unbalance responses of the rotor systems.