Power Flow Finite Element Analysis of Dynamic Systems: Basic Theory and Application to Beams

A power flow analysis has been developed for predicting the vibration response of dynamic systems to high frequencies at which the traditional finite element method is no longer practical. As compared to Statistical Energy Analysis, which predicts an overall vibration response of each dynamic subsystem, the power flow analysis enables one to predict the spatial variation of the vibration response within each subsystem, as well as the power flow and vibration response throughout the entire system. The formulation of the power flow analysis is based on a differential, control-volume approach and is shown to result in a partial differential equation of the heat conduction type which can be solved by applying the finite element method. Example applications to (1) an uncoupled beam and (2) two coupled beams are presented to illustrate the analysis.