Stochastic sensitivity analysis for structural dynamics systems via the second-order perturbation

The problem of dynamic structural response dependent on random variations of design parameters is presented in the paper. A variational formulation of the FEM equations of motion and the probability distribution of time instant stochastic sensitivity are described. The suggested perturbation technique is completely second-order accurate, unlike in conventional approach. For instance, three different structural systems, excited by a Heaviside impact, are implemented and discussed. Numerical results for the first two probabilistic moments of displacement sensitivity gradients are obtained by the mode superposition method. Concluding remarks show that dynamic sensitivity analysis in the stochastic context better describes the real structural response and allows us to find the appropriate design point.