Properties of Spectral Moments with Applications to Random Vibration

It is shown that many important reliability measures related to stationary random motion require the knowledge of two spectral parameters which depend on the first few moments of the reduced spectral density function. The first is a characteristic frequency, the second a unitless measure of the variability in the frequency content, i.e., of the bandwidth or the dispersion of the spectral density about its central frequency. For general stationary random processes, the spectral parameters are simply related to the mean square values of the process, its envelope, and their respective time derivatives. For Gaussian processes, other statistical properties, e.g., average barrier crossing rates, clump sizes, and maximum response characteristics, are importantly related to these parameters. A derivation is given for the spectral moments of the stationary response of damped linear multidegree-of-freedom systems for which classical modal analysis is possible.