Unsymmetrical Nonlinear Vibration Systems under Random Loading

Abstract

In this paper the author analyzes the effects of the unsymmetrical nonlinearity of restoring force and the mean square value of a random loading on the mean square value and spectrum of displacement in a vibration system which has a single degree of freedom. In this analysis an iteration method is applied to solve the equation of motion, assuming that the nonlinearity and loading have small values, and the approximate mean square value and spectrum of displacement are obtained from an equivalent loading spectrum. The random loading is expressed by Fouries series, and in the case of white spectrum an experiment is made using an analog computer.