Random load description In a random process, the amplitude can not be described as a function of time, because of its
probabilistic nature. However, certain statistical properties can be extracted from a signal sample, representing a realization of a random process, provided the latter is
ergodic. An important characteristics for the field of vibration fatigue is the amplitude
probability density function, that describes the statistical distribution of peak amplitudes. Ideally, the probability of cycle amplitudes, describing the load severity, could then be deduced directly. However, as this is not always possible, the sought-after probability is often estimated empirically.
Effects of structural dynamics . Random excitation of the structure produces different responses, depending on the natural dynamics of the structure in question. Different natural modes get excited and each greatly affects the
stress distribution in material. The standard procedure is to calculate
frequency response functions for the analyzed structure and then obtain the
stress responses, based on given loading or excitation. By exciting different modes, the spread of
vibration energy over a frequency range directly affects the durability of the structure. Thus the structural dynamics analysis is a key part of vibration-fatigue evaluation.
Vibration-fatigue methods Calculation of damage intensity is straightforward once the cycle amplitude distribution is known. This distribution can be obtained from a time-history simply by counting cycles. To obtain it from the
PSD another approach must be taken. Various vibration-fatigue methods estimate damage intensity based on moments of the
PSD, which characterize the statistical properties of the random process. The formulas for calculating such estimate are empirical (with very few exceptions) and are based on numerous simulations of random processes with known
PSD. As a consequence, the accuracy of those methods varies, depending on analyzed response spectra, material parameters and the method itself - some are more accurate than others. The most commonly used method is the one developed by T. Dirlik in 1985. Recent research on frequency-domain methods of fatigue-life estimation compared well established methods and also recent ones; conclusion showed that the methods by Zhao and Baker, developed in 1992 and by Benasciutti and Tovo, developed in 2004 are also very suitable for vibration-fatigue analysis. For narrow-band approximation of random process analytical expression for damage intensity is given by Miles. There are some approaches with adaptation of narrow-band approximation; Wirsching and Light proposed the empirical correction factor in 1980 and Benasciutti presented 0.75 in 2004. In 2008, Gao and Moan published a spectral method that combines three narrow-band processes. Implementation of those method is given in the
Python open-source FLife package. == Applications ==