Reliability Analysis on Fatigue Strength under Random Loading with Bimodal PSD

Abstract

To evaluate the cumulative fatigue damage under Gaussian random loading, the distribution of rainflow range must be evaluated from the random waves. It is considered difficult to evaluate the distribution of range from the geometry of the PSD of the waves except the narrow band random waves, the range distribution of which becomes Rayleigh distribution. As to the random waves with bimodal PSD, however, the authors have already shown that the range can be derived from the PSD analytically. The distribution of range can be represented by the ratio of two dominant frequencies and the ratio of two corresponding power.
In this paper, the property of fatigue damage evaluated by the proposed method is examined. And the fundamental equations necessary for reliability analysis are formulated. The derived equations are compared with the results of Monte-Carlo simulations and good agreements are obtained. Finally, several diagrams, which enable us fatigue design easily, are presented.