Resonance of engineering structures under stochastic vibration loadings is a primary cause of fatigue failure. Considering that cyclic loadings below the fatigue limit of the material contribute little to fatigue damage, the portion of the stress amplitude distribution that exceeds the fatigue limit is in focus in this paper, and a tail probability density distribution model of stress amplitude under band-limited stochastic vibration loadings is proposed. First, the response stress power spectral density functions under band-limited loadings are simulated by using the normal distribution and the Weibull distribution, respectively, and then the frequency domain signals are converted into time domain signals by adopting the inverse fast Fourier transform method. A two-parameter Weibull model of tail probability density distribution of stress amplitude is proposed, and the relationship between model parameters and power spectral moment parameters is given. Finally, the comparative analysis of the model accuracy and the vibration fatigue test of aluminum alloy notch specimen are carried out. It is demonstrated that the fatigue life predicted by the presented model is highly coincident with the results of tests and the time domain method.
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