Frequency domain stochastic response of structural systems with uncertain parameters: closed-form sensitivity

This study deals with the sensitivity analysis of the response of linear discretized structures with uncertain stiffness parameters subjected to stationary multi-correlated Gaussian random excitation. The proposed procedure relies on the use of the so-called rational series expansion (RSE), recently proposed by the authors as an alternative explicit formof the Neumann series expansion of the inverse of an invertible matrix with a modification of rank r. The RSE allows to derive approximate explicit expressions of the sensitivities of the probabilistic characteristics of the stationary stochastic response in the frequency domain by direct differentiation.The accuracy of the proposed procedure and computational issues related to sensitivity analysis are scrutinized through numerical results.