等価非ガウス励振化法による非ガウス性不規則励振を受ける線形系の過渡応答解析

抄録

The transient response moment analysis of a linear system subjected to non-Gaussian random excitation is carried out by using the equivalent non-Gaussian excitation method. The non-Gaussian excitation is prescribed by both probability density function and power spectrum. Since the excitation is described by the Ito stochastic differential^ equation, moment equations for the system response can be derived from governing equations for the excitation and the system. However, the moment equations are generally not closed due to the complex nonlinearity of the diffusion coefficient in the governing equation for the excitation. Therefore, using the equivalent non-Gaussian excitation method, the diffusion coefficient is replaced by the equivalent one, which is expressed by a quadratic polynomial. After the replacement of the diffusion coefficient, we can derive a closed set of the moment equations and obtain the time evolution of the response moments by solving the moment equations. In numerical examples, the analytical method is applied to a linear system under non-Gaussian excitation with the widely different probability distributions and bandwidth. Comparison between the analytical results and Monte Carlo simulation results illustrates the effectiveness of the equivalent non-Gaussian excitation method in transient response analysis.