A Variational Method for Approximating the Response of Nonlinear Stochastic Systems

A method is introduced for determining approximate properties of the response of nonlinear stochastic systems. The method is based in concept on the variational methods of mechanics and allows the consideration of classes of systems not readily subject to analysis by existing techniques. Three examples are presented illustrating the application to nonlinear systems with non-stationary inputs, non-Gaussian inputs and with time delay. The main limitation of the technique is the necessity for assuming a meaningful form for the approximate solution in terms of arbitrary random variables.