Frequency Response of Stochastic Dynamic Systems: A Modal Approach

摘要

A method to calculate the statistics of transfer functions from the probability density functions of the eigenvalues is proposed. Firstly, single-degree-of-freedom-systems are considered, and an approximation to the mean and variance is obtained using a hybrid Laplace's method and numerical integration method. Then, the method is extended to calculate the mean and variance of frequency response function of multiple-degrees-of-freedom dynamic systems. Proportional damping is assumed and the eigenvalues are considered to be independent. Results are derived for several probability density functions, including gamma, normal and lognormal distributions. The accuracy of the approach, for both single and multiple-degrees-of-freedom systems, is examined using the direct Monte Carlo simulation.