A Method for Double Random Vibration Analysis
A numerical procedure to compute the mean and covariance matrix of the random response of stochastic structures modeled by FE models is presented. With the help of Gegenbauer polynomial approximation, the calculation of dynamic response of random parameter system is transformed into an equivalent certainty expansion order system's response calculation. Non-stationary, non-white, non-zero means, Gaussian distributed excitation is represented by the well-known Karhunen-Loeve (K-L) expansion. The Precise Integration Method is employed to obtain the K-L decomposition of the non-stationary filtered white noise random excitation. A very accurate result is obtained by a small amount of K-L vectors with the vector characteristic of energy concentration, especially for the small band-width excitation. Correctness of the method is verified by the simulations.
J. Liao et al., "A Method for Double Random Vibration Analysis", Applied Mechanics and Materials, Vol. 577, pp. 119-124, 2014