Stochastic response of nonlinear structures with parameter random fluctuations

Abstract

The random response of a nonlinear structural system is examined when its parameters are experiencing random fluctuations with time. The treatment is based on the recent developments in the mathematical theory of stochastic differential equations. These include the Ito stochastic calculus and the Fokker-Planck equation approach to derive a general differential equation that describes the evolution of the statistical moments of the response coordinates. The differential equation is found to constitute an infinite coupled set of differential equations that are closed via two different closure schemes. The system response is determined in the neighborhood of internal resonance condition and for various random intensities of the system parameters. It is found that the random modal interaction is governed mainly by the internal resonance ratio and the stiffness fluctuation intensity. The effect of the random damping fluctuation on the system response is found to be very small compared to the stiffness fluctuation effect.