An algorithm for accurate evaluation of the fatigue damage due to multimodal and broadband processes

In a recent work, the author developed an accurate method for calculating the fatigue damage in a bimodal Gaussian process. The novelty of this method lies in its ability to incorporate two critical effects, which have been unrecognized in prior studies. This paper extends the bimodal technique to multiple modes. Through case studies of multimodal processes, the algorithm is found to produce highly precise damage estimates (∼1% error) when benchmarked against simulations. This is true even when the component frequencies are very close. Further, the multimodal method is used to analyze general broadband processes, by partitioning a given spectrum. Since the accuracy is relatively insensitive to frequency spacing, the errors emanate primarily from the narrowband assumption, and this can be controlled by employing more segments. It is shown that with a sufficient level of discretization, the predicted damage for a variety of spectral shapes is negligibly conservative, generally within 2%.