Linear systems subject to non-Gaussian α-stable processes

Methods are developed for calculating characteristic functions and mean upcrossing rates of the response of linear systems to α-stable input processes. The methods are based on the integral and series representations of these processes. The integral representation resembles the spectral representation of wide-sense stationary processes. The α-stable processes are non-Gaussian and have no moments of order two and higher. Therefore, classical methods of linear random vibration for calculating the mean and covariance functions of the response from the corresponding functions of the input do not apply. Applications are presented to illustrate the proposed methods of analysis.