THE VAN KAMPEN EXPANSION FOR LINKED DUFFING-LINEAR OSCILLATORS EXCITED BY COLORED NOISE

Abstract

This paper expands on previous work by Rodriguez and van Kampen, and by Weinstein and Benaroya. The original work by Rodriguez and van Kampen outlined a method of extracting information from the Fokker-Planck equation without having to solve the equation itself. In the van Kampen expansion, the Fokker-Planck equation is expanded about the random component of the response. This expansion is used to derive a series of first order differential equations in time for the moments of the response. These can then be solved for moments as a function of time. In the original work, this method was demonstrated on the case of a Duffing oscillator excited by white noise. Weinstein and Benaroya developed this method for the case of a Duffing ocsillator excited by colored noise, performed parametric studies on the system parameters, and verified their results by comparing them to Monte Carlo experiments. In this work, the van Kampen expansion is applied to systems of linked Duffing-linear oscillators excited by colored noise. Again, parametric studies are performed on the system parameters and the results compared to those of Monte Carlo experiments. It is found that the analytical results compare closely with the numerical results as long as the initial assumptions of the expansion are not violated. The closeness of the comparisons indicates that the van Kampen expansion is a valid technique for the study of this class of problem and is a useful tool in modelling offshore structures, plates in turbulent flows, and other fluid-structure interaction phenomena.