A probability density model of stress amplitude under bimodal vibration response

In order to improve the fatigue life prediction of engineering structures under bimodal vibration response stress power spectra, a new probability density model of stress amplitude is proposed in this paper, which is composed of an exponential distribution and a two-parameter Weibull distribution. Under ideal bimodal response stress power spectra with different bandwidths, the connection between the first three order moments of rain-flow amplitude distributions and the spectral parameters is found. Then, according to the equations between the first three order moments of stress amplitude distributions of the model and those of rain-flow amplitude dis-tributions, combined with the numerical optimization method, the relationship between model parameters and spectral parameters is established. Through comparative studies, the model in this paper leads to more accurate stress amplitude distributions and fatigue damage, which is very close to those obtained from time domain approach. Through the stochastic vibration fatigue test of aluminum alloy notched specimens, the high accuracy of the proposed model for estimating fatigue life is further verified.