Stochastic beam equations under random dynamic loads

The fourth order partial differential equation representing beams under random loading is considered. A general solution for this equation is obtained using the eigenfunction and variation of parameters techniques. Also the average and the variance of the beam deflection, shear and bending moment are obtained. The load is divided into a deterministic function and a randomly perturbed function representing the expected error in the deterministic load. The general closed form solution is obtained in stochastic integral terms. Some important statistical moments of the solution process are computed and illustrated.