Explicit sensitivities of the response of discretized structures under stationary random processes

This study presents a semi-analytical approach for the sensitivity analysis of the response of linear discretized structures subjected to stationary multi-correlated Gaussian random excitation. The proposed procedure relies on the use of the so-called rational series expansion (RSE), recently derived by the authors for evaluating in approximate explicit form the inverse of a matrix with small rank-r modifications. The RSE allows to determine the mean-value and power spectral density function of the response as approximate explicit functions of the design parameters. Direct differentiation of these functions with respect to the design parameters provides approximate analytical expressions of the sensitivities of the probabilistic characteristics of the stationary stochastic response in the frequency domain. Numerical results concerning different structural systems under random excitation are presented to demonstrate the accuracy and efficiency of the proposed procedure.