THE SPECTRAL RESPONSE OF SINGLE-DEGREE OF FREEDOM SYSTEMS WITH STATIONARY RESPONSE

Abstract

In many practical applications the system of concern has non-linearities, whitch must be taken into account if one is to predict its performance in a realistic way. For such non-linear problems the classical linear theory, which can be found in a number of text books, is not directly applicabile and new techniques are required. If a non-linear mathematical model of the system under consideration is adopted, together with a random process model of the excitation, then is faced with the problem of predicting the system response. A method for estimating the power spectral density of the stationary response of oscillator with a nonlinear restoring force subjected to external wide band noise excitation has been proposed. The efficiency of the method is checked by comparing results with those numerical simulations. The basic idea of the statistical linearization approach is to replace the original nonlinear system by a linear one. This is done in such a way that the difference between the two systems is minimised in some statistical sense. In this way, the parameters of the linearised system are determined.