The use of frequency domain parameters to predict structural fatigue
The work in this thesis outlines the use of power spectral density data for estimating the Fatigue Damage of structures or components subjected to random loading. Since rainflow cycle counting has been accepted as the best way of estimating the fatigue damage caused by random loadings, an obvious target was a method of obtaining the rainflow range distribution from the PSD. Such a solution is derived in this thesis. It forms the major part of the work presented and appears in chapter 5. The rest of the thesis deals with the following topics; Chapter 3 first presents some empirical solutions developed by other authors for the prediction of rainflow ranges from PSD's. An empirical solution developed by Dirlik in 1985 is then used to investigate the effect that stresses contained within a given frequency range have on fatigue damage when there are other frequencies present in the PSD plot. This can be thought of as 'fatigue damage potential'. Interactions between stresses in different frequency intervals are investigated and it is shown that the fatigue damage potential of one frequency interval is dependent not only on the magnitude of that interval but on the magnitudes of other frequency intervals present. This 'Interaction' effect within the PSD plot, is of specific interest because it can be used to determine the change of fatigue damage for any given structure or component when parts of the signal or PSD plot are altered. Chapter 4 is concerned with methods of regenerating a signal from a PSD in the form of a set of peaks and troughs. Work by Kowalewsld in 1963 is introduced which gives a solution for the joint distribution of peaks and troughs. This distribution can be used to generate a continuous set of adjacent peaks and troughs, of any length, using Monte-Carlo techniques. Approximations in this result are discussed, in comparison with the (distribution of times between) zero crossings problem. An improvement to this joint distribution of peak and troughs is given which uses an empirical solution for the distribution of 'ordinary ranges' (ranges between adjacent peaks and troughs). Chapter 5 forms the major part of the original work presented in this thesis and outlines a theoretical solution for the prediction of rainflow ranges using statistics computed directly from the power spectral density plot. The rainflow range mechanism is broken down into a set of logical criteria which can be analyzed using Markov process theory. The dependence between extremes in this instance is modelled using the prediction of the joint distribution of peaks and troughs proposed by Kowalewsld, and shown in chapter 4. Chapter 6 deals with the fatigue damage assessment and stress history determination of components when only limited samples of the service data are available. An investigation is carried out into the relative merits of time and frequency domain techniques. In particular, the effect of finite sample length was investigated with particular reference to the variance of fatigue predictions using both a rainflow count on a limited time sample and a rainflow count produced directly from a PSD of the same time sample. The frequency domain approach is shown to be at least as accurate as the direct time domain approach. Chapter 7 deals with one specific area where the methods presented in this thesis are applicable, namely, dynamically sensitive offshore structures. Various methods of fatigue damage assessment are highlighted, followed by a detailed description of the 'deterministic/spectral' approach. Many factors which have not previously been recognised are investigated and shown to have significant effect, for instance, tidal effects.