Recursive expressions for random response of nonlinear systems

Abstract

Recursive expressions for variance of response of general nonlinear systems subjected to nonstationary random disturbances are obtained by the stochastic central difference method. The technique is illustrated by deriving the explicit recursive variance of response for a Duffing oscillator. It is intrinsically different from that presented earlier by the present author in that it is derived without recourse to the statistical linearization technique. In parallel, a new stochastic central difference-cumstatistical linearization technique is presented. Computed results using the two approaches presented in this paper are compared with those of digital simulation. It is concluded that the two approaches are accurate, relatively much more economical to employ, and can handle highly nonlinear cases. Furthermore, they are simple to implement in a digital computer and therefore can be easily used to verify results using other techniques.