Analyzing Random Vibration Fatigue

Determining the fatigue life of parts under periodic, sinusoidal vibration is a fairly straightforward process in which damage content is calculated by multiplying the stress amplitude of each cycle from harmonic analysis with the number of cycles that the parts experience in the field. The computation is relatively simple because the absolute value of the vibration is highly predictable at any point in time. Vibrations may be random in nature in a wide range of applications, however, such as vehicles traveling on rough roads or industrial equipment operating in the field where arbitrary loads may be encountered. In these cases, instantaneous vibration amplitudes are not highly predictable as the amplitude at any point in time is not related to that at any other point in time. As shown in Figure 1, the lack of periodicity is apparent with random vibrations. The complex nature of random vibrations is demonstrated with a Fourier analysis of the random time–history shown in Figure 2, revealing that the random motion can be represented as a series of many overlapping sine waves, with each curve cycling at its own frequency and amplitude. With these multiple frequencies occurring at the same time, the structural resonances of different components can be excited simultaneously, thus increasing the potential damage of random vibrations.