METHOD OF RANDOM VIBRATION FOR THE DUFFING OSCILLATOR WITH NON-LINEAR ELASTIC CHARACTERISTIC AND EXTERNAL WHITE NOISE VEXCITATION

Abstract

The statistical linearization technique can also tackle a wide variety of problems and also provides approximate information on the frequency domain characteristics of the stochastic response. In this technique, a linear model, which optimally ts the original, nonlinear system (in some statistical sense), is constructed. The cause for this underestimation of the variance can be found by comparing accurate, simulated frequency domain characteristics with those determined using the linear model.This approximate representation of the system leads to estimates of the response spectrum that agree extremely well with those obtained by direct numerical simulation of the governing equation.