Beams on random elastic supports

Abstract The fourth-order differential equation of a beam resting on elastic supports is highly dependent upon the modulus of subgrade reaction, k. In general, the value of k is random; consequently, a beam resting on random supports is represented by a random differential equation of random coefficient. This differential equation has no exact solution; accordingly, approximate solution is recommended. The statistical moments of the solution process are expanded in terms of the stochastic scale parameter ζ and evaluated by using successive approximations