Non-stationary random response of a finite cable

Abstract

Numerous problems of current concern involve the designs of aerodynamic systems which either travel at high speeds or contain structural elements which are excited by moving pressure fluctuations. In a number of recent papers responses of dynamic systems to random excitation have been considered. The appropriate theory for calculating the mean square response of linear systems to both stationary and non-stationary random excitation is well known [1–7]. In this paper, the mean square response of a finite cable to non-stationary random excitation is considered. The non-stationary random excitation is of the form s( t) = e( t) α( t), where e( t) is a well defined envelope function and α ( t) is the Guassian, narrow band, stationary part of the excitation which has zero mean. Both the unit step and rectangular step functions are used for the envelope function, and both white noise and noise with an exponentially decaying harmonic correlation function are used to prescribe the statistical property of the excitation. The results obtained are shown to be a complete expression for the mean square response when checked for accuracy by reduction to expressions previously obtained by Lyon [4]. It is felt that these results will aid the design of both linear and two-dimensional aerodynamic systems excited by random pressure fluctuations.