Response of Beam to Stochastic Boundary Excitation

A closed-form solution is presented for the covariance kernel of the transient response of a damped Bernoulli-Euler beam with arbitrary boundary conditions to correlated stochastic excitation applied at the boundaries. The analytical results are applied to the case where the autocorrelation function of the excitation resembles that of a wide class of input functions including earthquake excitations. The mean-square transient response at arbitrary locations along the beam is evaluated, and the effects of various system parameters are determined. It is shown that depending on the beam characteristics, the spectral width of the input, and the delay time involved in the wave propagation between supports, the mean-square response of the beam can be dramatically influenced.