Abstract
In this article, we are analyzing a differential equation with random variable. Our new technique based on the combination of the transformation method with equivalent linearization theory and minimizing the expectation of the square error to evaluate the probability density function and the power spectral density of the solution. The accuracy of the procedure depends on the bandwidth of the excitation and of the way to decompose the nonlinear restoring force in one linear component plus a nonlinear component. Exact solutions for a non-linear system under random excitation are rare. It is known that even under ideal white noise excitation, only for certain types of non-linear systems, the exact probability density function of the response in the steady state can be obtained [1]. Usually the power spectral density of the input is non-white and the probability density function is taken to be Gaussian to seek an approximate solution through equivalent linearization techniques [2].
Keywords: Non-Linear System, White Noise, Response, Equivalent Linearization, Random Vibration