Characteristics of Response to Nonstationary White Noise: Applications

Abstract

In the companion paper new methods were developed to obtain exact and approximate second‐order statistics of the response of linear systems to modulated white‐noise excitation. In this paper the methods are used to evaluate characteristics of oscillator response to two basic modulations. Closed‐form expressions are obtained for the variance, mean zero‐crossing rate, and bandwidth of the response to suddenly‐applied excitation and numerical values are computed for an exponentially‐modulated excitation. Both analytical and numerical comparisons re‐veal that the approximate method of analysis is considerably simpler than the exact method, yet accurately retains the dominant features of the nonstationary response characteristics. The results are subsequently applied to the first‐passage problem using continuous and discrete forms of the response envelope. Good agreement with simulation results is observed in all cases.