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.
uncertain-but-bounded parameters complex interval analysis stationary gaussian random excitation frequency domain approach shermanmorrisonwoodbury formula