RANDOM VIBRATION OF FLEXIBLE, UNCERTAIN BEAM ELEMENT

A stochastic finite element method is developed to analyze the random responses of geometrically nonlinear beams and frames with combined uncertain material and geometric properties under simultaneous spatial and temporal random excitations. The method is based on an equivalent linearization scheme, combined with the mean-centered second-order perturbation technique and the modal expansion approach. The procedure can be straightforwardly extended to incorporate other existing finite elements. Examples include large-amplitude free vibration and dynamic random response of three simply supported beams and a portal frame with combined uncertain material and geometric properties. For the case of beams and frame with no structural uncertainties, the results obtained are in good agreement with alternative solutions. For the case of beams and frame with structural uncertainties, alternative representative results are also obtained using Monte Carlo simulation to compare and validate the present solution and method.