STOCHASTIC DYNAMICS OF GEOMETRICALLY NONLINEAR STRUCTURES WITH RANDOMPROPERTIES SUBJECT TO STATIONARY RANDOM-EXCITATION

A non-linear stochastic finite element formulation for the stochastic response analysis of geometrically non-linear, elastic two-dimensional frames with random stiffness properties and random damping subject to stationary random excitations is derived, utilizing deterministic sha pe functions and random nodal displacements. Hence, a consistent weigh ted integral method has been applied for the discretization of the ran dom fields of beam elements. The discretized second order non-linear s tochastic differential equations with random coefficients are then sol ved applying the total probability theorem with a mean-centered second order perturbation method in the frequency domain to evaluate the unc onditional 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 eigenmodes and equivalent linearization with Gaussian closure a re applied. Sample frames are solved to illustrate the validity range of the second order perturbation random vibration analysis in terms or variability of the random damping ratios and the random bending rigid ity held as well as the correlation length of the random bending rigid ity field. Computed results are compared with the ones obtained from e xtensive Monte Carlo simulations. (C) 1996 Academic Press Limited