Filter Approximations for Random Vibroacoustics of Rigid Porous Media

An approximate efficient stochastic dynamics technique is developed for determining response statistics of linear systems with frequency-dependent parameters, which are used for modeling wave propagation through rigid porous media subject to stochastic excitation. This is done in conjunction with a filter approximation of the system frequency response function. The technique exhibits the following advantages compared to alternative solution treatments in the literature. First, relying on an input-output relationship in the frequency domain, the response power spectrum matrix is integrated analytically for determining the stationary response covariance matrix, at zero computational cost. Second, the proposed filter approximation facilitates a state-variable formulation of the governing stochastic differential equations in the time domain. This yields a coupled system of deterministic differential equations to be solved numerically for the response covariance matrix. Thus, the non-stationary (transient) response covariance can be computed in the time domain at a relatively low computational cost. Various numerical examples are considered for demonstrating the accuracy and computational efficiency of the herein developed technique. Comparisons with pertinent Monte Carlo simulation data are included as well.