A study of uncertainty in applications of sea to coupled beam and plate systems, part I: Computational experiments

Abstract

Computational studies of the effects of random geometric perturbations of coupled beams and plates on frequency-band average vibrational power flow, and on derived coupling loss factors, are presented. Complementary experimental results will be presented in Part II of the paper. The results indicate that the two principal parameters which control the variability of power flow, and the associated coupling loss factor, are the modal overlap factors of the uncoupled subsystems and the number of coupled modes of the total system which are resonant in the frequency band considered. It is confirmed that the commonly employed “travelling wave” estimate of coupling loss factor generally exceeds the actual value when the average modal overlap factor is much less than unity. Under conditions of low modal overlap the normalized variance of the power flow tends significantly to exceed that of the perturbed geometric parameter, while that of the associated coupling loss factor can be of the order of unity: both variances become small when the modal overlap factor exceeds unity. Under conditions of low modal overlap, normally distributed geometric variations generate highly non-normal distributions of power flow and coupling loss factor. It is found that it is necessary to have at least five modal resonance frequencies in a band for stable estimates of coupling loss factor to be obtained. A problem of potential concern to analysts of variance in SEA is that the relationship between the variance of “input” and “output” quantities is not, in general, linear, thereby limiting the general validity of conclusions reached by specific computational or experimental studies. A conclusion of practical significance for experimental evaluation of coupling loss factors is that value derived from tests on one physical sample of a class of system may be quite unrepresentative of the ensemble-average value when modal overlap factors are small.