Closed-form sensitivities of the frequency domain response of structural systems with interval uncertainties

The present study deals with the interval sensitivity analysis of linear discretized structures with uncertain-but-bounded parameters subjected to stationary multi-correlated Gaussian stochastic processes. The proposed procedure allows to derive approximate explicit expressions of the interval sensitivities of the mean-value vector and Power Spectral Density (PSD) matrix of the interval stationary stochastic response. The core of the procedure is the so-called Interval Rational Series Expansion (IRSE), recently proposed by the authors as an alternative explicit expression of the Neumann series expansion for the inverse of a matrix with a rank-r modification and properly extended to handle also interval matrices. Numerical results pertaining to a truss structure with interval Young’s moduli are presented to demonstrate the effectiveness of the proposed method as well as to show the great value of interval sensitivity analysis for design purposes.