Prediction and Measurement of the Proportionality Constant in Statistical Energy Analysis of Structures

Abstract

The fundamental equation of statistical energy analysis (SEA) states that the average power flow between two coupled vibrating systems is proportional to the difference in their average modal energies. Under certain circumstances, one can estimate the proportionality constant by modifying system boundary conditions on the separated systems and calculating or measuring changes in the systems. Newland's estimate, based upon blocking part of the system, is reexamined and limitations are discussed. Three alternative methods which circumvent blocking are presented. They are based, respectively, upon (1) natural frequency shift due to addition of mass; (2) mechanical input impedance; and (3) mean square velocity response at the excitation point due to random excitation. The new methods were applied to predict power flow in experiments on coupled beams and on coupled plates. One or both parts of the coupled structures were then excited by external random sources, and power flow through the coupling was measured directly as a product of force with velocity. The fundamental SEA relation was supported by the measurements, which included the null power point where the difference in average modal energies was zero. Measured and predicted proportionality constants are compared. [This work was supported in part by the National Aeronautics and Space Administration.]