Transient Dynamics of Stochastically Parametered Beams

The problem of determining the statistics of the transient response of randomly inhomogeneous beams is formulated. This is based on the use of stochastic dynamic stiffness coefficients in conjunction with the fast Fourier transform algorithm. The dynamic stiffness coefficients, in turn, are determined using a stochastic finite-element formulation that employs frequency-dependent shape functions. The approach is illustrated by analyzing the response of a random rod subject to a boxcar type of axial impact and, also, by considering the flexural response of a randomly inhomogeneous beam resting on a randomly varying Winklerʹs foundation and subjected to the action of a moving force. A discussion on the treatment of system property random fields as being non-Gaussian in nature is presented. Also discussed are the methods for handling nonzero initial conditions within the framework of the frequency domain response analysis employed in the study. Satisfactory comparisons between the analytical results and simulation results are demonstrated.