DIRECT SPECTURM ANALYSIS OF THE STATE SPACE FOR RANDOM VIBRATION OF MDOF LINEAR DAMPED SYSTEM

This paper proceeds from the general case of the unsymmetric linearized multi-degrees of free-dom(MDOF)systems.By adopting the general complex modal theory of the state space,the response analysis for a sys-tem subjected to random excitation of the same source is carried out using as a kind of direct spectrum analysis method infrequency domain.With the input of power spectral density function given,the explicit expression of the power spectraldensity function matrix of the output response can be obtained.By taking Fourier inverse transform,the integrated expres-sions of the correlation function matrix and of the spectrum moment matrix are obtained.Comparing with the time domainmethod,this method enjoys the merit of visualization and avoids the procedure of transformation from the obtained re-sponse correlation function to be solved for the output spectrum utilizing Fourier transform.This paper has extended theapplication range of the traditional frequency domain analysis method.The mean square values and variety of statistical val-ues can be obtained conveniently.This method and the time domain method are different in approach but equally satisfac-tory in their results.