STATISTICS OF ENERGY FLOWS IN SPRING-COUPLED ONE-DIMENSIONAL SUBSYSTEMS

This paper considers the problem of determining the statistical fluctu ations occurring in the vibrational energy flow characteristics of a s ystem of two multimodal, random, one-dimensional subsystems coupled th rough a spring and subject to single frequency forcing. The subsystems are modelled either as transversely vibrating Euler-Bernoulli beams o r as axially vibrating rods. The masses of the subsystems are modelled as random variables. The calculations of energy flows are based on an exact formulation which uses the Green functions of the uncoupled sub systems, which, in turn, are expressed as summations over the uncouple d modes. Factors influencing the number of modes contributing to the r esponse statistics at any specified driving frequency are investigated . A criterion for identifying the driving frequency beyond which the m ean power spectra become smooth is proposed. Empirical procedures are developed to predict the 5 % and 95 % probability points given knowled ge of the first two moments of the response. The work reported here fo rms part of a long term study into the reliability of statistical ener gy analysis (SEA) methods.