Statistics of energy flows in spring-coupled one-dimensional subsystems

Abstract

This paper considers the problem of determining the statistical fluctuations occurring in the vibrational energy flow characteristics of a system of two multimodal, random, one-dimensional subsystems coupled through a spring and subject to single frequency forcing. The subsystems are modelled either as transversely vibrating Euler- Bernoulli beams or 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 subsystems, which, in turn, are expressed as summations over the uncoupled modes. Factors influencing the number of modes contributing to the response statistics at any specified driving frequency are investigated. A criterion for identifying the driving frequency beyond which the mean power spectra become smooth is proposed. Empirical procedures are developed to predict the 5 % and 95 % probability points given knowledge of the first two moments of the response. The work reported here forms part of a long term study into the reliability of statistical energy analysis (SEA) methods.