入力の高次自己相関関数を用いた非ガウス性不規則入力を受ける線形系の過渡応答統計量の解析

抄録

In the previous study, the stationary and transient response characteristics of linear systems subjected to non-Gaussian random excitation were investigated by Monte Carlo simulation. It was revealed that the response characteristics are strongly dependent upon the bandwidth of the excitation power spectrum. Furthermore, it was also found that in the transient state, the degree of non-Gaussianity of the response caused by non-Gaussian random excitation changes periodically. These response characteristics were examined numerically. For this reason, analytical considerations (e.g. Which terms of the changing periods the response statistics consists of and which of them is dominant?) have not yet been made. Therefore, in this research, the analytical solutions of transient response statistics of a linear system under non-Gaussian random excitation are derived to investigate the response characteristics in detail. In order to derive the analytical solutions, first, the higher-order autocorrelation functions of the random excitation are obtained using the Markov property. Then, using the higher-order autocorrelation functions of the excitation, the transient response statistics are derived based on the convolution integral of the excitation and the impulse response function of a linear system. Finally, the transient response statistics are separated according to the changing periods, and the dominant term and period of the statistics are investigated.