Bounds for the stationary stochastic response of truss structures with uncertain-but-bounded parameters

The aim of the present paper is to determine the region of the probabilistic characteristics of the stationary stochastic response (mean-value vector, power spectral density function and covariance matrix) of truss structures with uncertain-but-bounded parameters under stationary multi-correlated Gaussian random excitation via interval analysis. The main steps of the proposed procedure are: i) to express the stiffness, damping and mass matrices of the structural system as linear functions of the uncertain-but-bounded parameters; ii) to split the probabilistic characteristics of the nodal interval stationary stochastic response, evaluated in the frequency domain, as sum of the midpoint and deviation values; iii) to evaluate in explicit approximate form the parametric interval frequency response function matrix. The effectiveness of the presented procedure is demonstrated by analyzing a truss structure with uncertain-but-bounded axial stiffness and lumped masses subjected to stationary multi-correlated Gaussian wind excitations.

► Trusses with interval parameters under stationary random excitation are analyzed. ► An improvement of the “ordinary” complex interval analysis is introduced. ► The interval transfer function matrix is evaluated in explicit approximate form. ► The bounds of the stationary response probabilistic characteristics are evaluated. ► The comparison with the exact bounds proves the accuracy of the proposed method.