Response of structural systems with uncertain-but-bounded parameters under stationary stochastic input via interval analysis

The aim of the present paper is to determine the region of second-order statistical moments of the response of linear finite element modelled structural systems with uncertain-but-bounded parameters under stationary Gaussian random excitation via interval analysis. The key idea of the proposed approach is to express the random response by using a first-order approximation conceptually different from the one assumed in the context of the traditional interval perturbation method. Specifically, the covariance vector is split as sum of two aliquots: the midpoint or nominal solution and a deviation. The latter is evaluated by superimposing the contributions obtained considering one uncertain-but-bounded parameter at a time. Once the linear algebraic equations ruling the midpoint solution and the deviations due to the uncertain parameters separately taken are solved, the bounds of the covariance vector are determined by handy formulas. The effectiveness of the presented procedure is demonstrated by analyzing a shear-type frame with uncertain Young’s modulus subjected to stationary white noise excitation.