Stochastic Dynamics of Nonlinear Structures with Random Properties Subject to Stationary Random Excitation
A nonlinear stochastic finite element formulation for the stochastic response analysis of geometrically nonlinear, elastic 2-dimensional frames with random stiffness and damping properties subject to stationary random excitation is derived utilizing deterministic shape functions and random nodal displacements. The discretized second order nonlinear stochastic differential equations with random coefficients are solved applying the total probability theorem with a mean-centered second order perturbation method in the frequency domain to evaluate the unconditional statistics of the response. Zeroth, first and second order perturbations are computed using a spectral approach in which a system reduction scheme to the modal subspace expanded by the deterministic linear eigen- modes and equivalent linearization with Gaussian closure are applied. Sample frames are solved and the results are compared with the ones obtained from extensive Monte Carlo simulations.
KeywordsBeam Element Nonlinear Structure Unconditional Variance Stochastic Finite Element Method Basic Random Variable
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