SPECTRAL RESPONSE FOR THE DUFFING OSCILLATOR WITH NON-LINEAR ELASTIC CHARACTERISTIC

Abstract

The statistical linearization techniques considered in this paper are all based on the concept of using an equivalent linear system to compute the necessary expectation which occur in the expressions for the equivalent linear parameters. This article explains the method of statistical linearization and its use in solving random vibration problems. Numerous examples, drawn from a wide variety of engineering problems, offer a comprehensive view of the methods practical applications. This paper include general equations of motion for the Duffing oscillator and the representation of non-linearityes, probability theory, elements of linear random vibration theory and statistical linearization for simple systems with stationary response oscillator. 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.