Solution of the nonlinear transverse vibration problem of a beam on elastic foundation using the Adomian decomposition method

Abstract

We apply the Adomian decomposition method to solve the nonlinear vibration problem of a geometrically nonlinear beam on an elastic foundation under the action of a transverse dynamic load. We model the elastic foundation as a spring continuously distributed over the span of the beam. We consider two cases. In the first case, we consider the spring to be linear and in the second case we consider the spring to be nonlinear. Approximate analytical solution obtained from the Adomian decomposition method is compared with the finite element solution. Limitation of the Adomian decomposition method is explored.