On the comparison of the Gaussian heuristic with the statistical linearization methods in random vibrations

Abstract

In this paper the cumulate description of random processes is used for obtaining general formulae of the Gaussian heuristic method in single-degree-of-freedom and multi-degree-of-freedom systems. These formulae can be easily applied to particular cases. Whereby he Gaussian heuristic method and the statistical linearization method are compared. It can be shown, that if the solution process and the excited process are assumed to be jointly Gaussian, then these two methods are equivalent. Besides, on the basis of the Gaussian heuristic method, the statistical linearization coefficients are presented by more simple expressions than that in the papers [1,7].