Stochastic analysis of structures with uncertain-but-bounded parameters

This study deals with the analysis of linear structures with slight variations of the structural parameters subjected to zero-mean Gaussian random excitations. Under the realistic assumption that the available experimental data are insufficient or incomplete to apply a probabilistic approach, the fluctuating properties are modeled as uncertain-but-bounded parameters via Interval Analysis. A novel procedure for estimating the lower and upper bounds of the second-order statistics of the response is proposed. The key idea of the method is to split the random response as sum of two aliquots: the midpoint or nominal solution and a deviation. The latter is approximated by superimposing the responses obtained considering one uncertain-but-bounded parameter at a time. After some algebra, the sets of first-order differential equations ruling the midpoint covariance vector and the deviations due to the uncertain parameters separately taken are obtained. Once such equations are solved, the region of the response covariance vector is determined by handy formulas. To validate the procedure, a three-storey shear-type frame with uncertain Young's modulus under uniformly modulated white noise excitation is analyzed.