Monte Carlo Solution of Nonlinear Vibrations

A Monte Carlo technique is presented which can effectively be used for nonlinear response analysis of a structure subjected to a random pressure field undergoing large deflections. The pressure field is idealized as a multidimensional Gaussian process with mean zero and homogeneous both in time and space. The response analysis is performed in the time domain by numerically simulating generalized forces rather than in the frequency domain. The solution satisfies the boundary conditions and the differential equation in a Galerkin sense. Two numerical examples involving large deflections of a string and a plate are worked out. The result indicates that the present method indeed provides a powerful tool in solving nonlinear structural response problems under random excitations.