线性随机参变振动的谱分解法

本文是1]文的一个发展.考虑如下的随机方程:(t)+2β?(t)+ω₀2Z(t)=(a₀+a_lZ(t)).I(t)+c,激励I(t)和响应到Z(t)都是随机过程,并设它们相互独立.如1],设I(t)=a(t)I0(t),a(t)是已知的时间函数,IO(t)是平稳随机过程.本文考虑了以上随机方程的谱分解形式,数值求解方法以及一些特殊情况的解式.

A Spectral Resolving Method for Analyzing Linear Random Vibrations with Variable Parameters

This paper is a development of Ref.1].Consider the following random equation:(t)+2?(t)+₀2Z(t)=(a₀+a_lZ(t)).I(t)+c,in which excitation I0(t)and response Z(t)are both random processes, and it is proposed that they are mutually independent.Suppose that I(t)=a(t)I0(t),a(t)is a known function of time and IO(t)is a stationary random process.In this paper, the spectral resolving form of the random equation stated above, the numenca solving method and the solutions in some special cases are considered.