Extremes of Gaussian Processes with Bimodal Spectra

Abstract

An approximate solution is developed for the extreme‐value distribution of a stationary Gaussian process with a spectral density function that exhibits two well‐separated modes. Processes of this type arise in the analysis of the combined dynamic response to two loads or to one load that excites two of a structure's modes of vibration. Spectral moments of each of the modes taken separately are used to characterize the process; two envelope processes are then used to approximate the extreme value distribution. The proposed distribution is compared with other approximations and with results from Monte Carlo simulations.