Response statistics and variance for a single SEA subsystem: Theory and experiment

Abstract

This paper is concerned with the ensemble statistics of the response of a single SEA subsystem. A general theory is presented for (i) the statistics of the point-to-point transfer function, and (ii) the statistics of the kinetic energy when the forcing consists of a specified number of incoherent point loads. The theory for case (i) is based on a modified version of the work of Schroeder, while that for case (ii) is based on point process theory and the Gaussian Orthogonal Ensemble. The theory has been applied to a plate with attached masses, and the results have been compared with those arising from a supporting experimental program. The experimental data was obtained by taking a single plate and considering 19 different configurations of the attached masses. For each configuration 5 drive points were considered, and the response was recorded at 13 locations, thus allowing the kinetic energy to be estimated. Excellent agreement between theory and experiment is reported and the validity of a simple formula for the variance of the energy is confirmed. One key finding concerns the influence of the nature of the loading on the mean and variance of the response: for example, five incoherent drive points produce the same mean energy as 'rain-on-the-roof' forcing, but the variance produced by the two types of loading is very different.