DAMPING ESTIMATION OF PLATES JOINED AT A POINT USING STATISTICAL ENERGY ANALYSIS

Abstract

The loss factors and coupling loss factors of a 2-plate, coupled system were estimated using the Statistical Energy Analysis methodology. In particular the Power Input Method (P.I.M.) and the Transient Statistical Energy Analysis Method (T.S.E.A.) were applied to both steady state and transient excitation cases. The effects of various process parameters such as frequency resolution, frequency bandwidths, type of hammer tip and measurement points on the estimated loss factors were also investigated for 3 different levels of damping. Possible reasons for the occurrence of negative coupling loss factor estimations using the T.S.E.A. method have been discovered to be the flexibility of the joint between the plates and the frequency resolution of the measured data. The effect of frequency resolution and damping on the estimated loss factors was examined both numerically and experimentally. First, a two degree of freedom (2-DOF) system was numerically simulated with varying model loss factors of 0.1%, 7.5% and 75% and frequency resolutions of 0.05 Hz, 0.2Hz and 1 Hz. The estimated loss factors were found to be highly dependent on the frequency resolution only in the lightly damped case. Experiments were then performed on 2 Aluminum plates coupled at a point, varying both the damping (by adding constrained layer damping) and the frequency resolution. It was seen that the coupling loss factors were not dependent on the damping levels, whereas the loss factors increased as the damping increased as expected. As the frequency resolution was decreased the loss factors in some frequency bands, especially the lower frequency bands, tended to negative values. The loss factors estimated, using the power input method, were in good agreement with both shaker and hammer excitations. Modal density and modes in band were also calculated and compared with the theoretical results. Significant variation between the theoretical values and the experimental values was seen only in the `No damping' case and only in the lower frequency bands. The main aims of using the T.S.E.A. method were to interpret the results from the dissertation by M. L. Lai, to find out the practical limitations of the method and to establish the degree of agreement of the asymptotic loss factor estimations with respect to the P.I.M. A numerical simulation was run on a 2-DOF system to show how the loss factor varies with time for a transient hit. It also showed that the theoretical coupling coefficients were off by more than 150% when a double hit occurs. Experiments were conducted to check for the effects of frequency resolution and frequency bandwidth on the estimated coupling loss factors. An increase in the damping levels of the plates caused the number of negativities in the "apparent time varying coupling loss factor" estimates to decrease while simultaneously decreasing the time taken to reach an asymptotic value. Possible reasons for the occurrence of negative coupling loss factors were discussed.