Flexible Beam and Frame Elements under Nonwhite and Nonzero Mean Loads

Abstract

A finite element formulation combined with stochastic linearization and normal mode methods is developed for the study of geometrically nonlinear random vibration responses of beam and frame structures subjected to simultaneously spatial and temporal Gaussian stationary nonwhite and nonzero mean random excitations. Examples include dynamic random responses of simply supported beams, clamped‐clamped beams, a simply supported beam on an elastic foundation, and a fixed‐end portal frame under various random loadings. To compare and validate the present formulation and solutions, results are compared with alternative analytical solutions whenever available. The Monte Carlo simulation method is also used to generate solutions to compare with some of the present results when alternative solutions are not available.