Nonlinear Vibrations of Systems under Random Loading

Abstract

In this paper it is analyzed what influence the symmetrical nonlinearity of restoring force and the mean square value of a random loading have upon the mean square value and aspectrum of displacement in a vibration system having 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 first approximate mean square value and spectrum of displacement are derived. In the case of a hard spring, the mean square value of deflection is smaller than that in the case of linear spring, while in the case of a soft spring it is larger than that in the case of a linear spring. These phenomena are remarkable when the system is under heavy loading. The spectrum of displacement has a peak value at the higher frequency in the case of a hard spring and at the lower frequency in the case of a soft spring.