Damping Estimation of Plates for Statistical Energy Analysis

Abstract

The Power Input Method (P.I.M.) and the Impulse Response Decay Method (I.R.D.M.) are used to evaluate how the accuracy of damping loss factor estimation for plates is affected with respect to various processing parameters, such as the frequency resolution, the frequency bandwidth, the number of measurement locations, and the signal to noise ratio. In several computational experiments, accuracy is assessed for a wide range of damping loss factors from low (0.1%) to moderate (1%) to high (10%). A wide range of frequency is considered, including "low frequencies" for which modal density is less than one per band. The Power Input Method (P.I.M.) is first validated with computational studies of an analytical single degree of freedom oscillator. Experimental loss factor estimates for plates (multiple degree of freedom systems) are also computed using the P.I.M. algorithm. The P.I.M. is shown to estimate loss factors with reasonable accuracy for highly damped plates in the 300 Hz - 4000 Hz, wherein modal density exceeds unit value. In this case "reasonable accuracy" means the estimated loss factors are within 10% of those predicted by the impulse response decay method. For lower damping levels the method fails. The analytical Impulse Response Decay Method (I.R.D.M.) is validated by the use of two computational models: a single degree of freedom oscillator and a uniform rectangular panel. The panel computational model is a finite element model of a rectangular plate mechanically excited at a single point. The computational model is used to systematically evaluate the effect of frequency resolution, frequency bandwidth, the number of measurement points used in the computations, and noise level for all the three levels of damping. The "optimized" I.R.D.M. is shown to accurately estimate damping in plate simulations with low to moderate levels of damping with a deviation of no more than 2% from the known damping value. For highly damped plates the I.R.D.M. tends to under-estimate loss factors at high frequency. Experimental loss factor estimation for an aluminum plate with full constrained layer damping treatment, classified as a highly damped plate, and an undamped steel plate, classified as a lightly damped plate are computed using the "optimized" I.R.D.M. algorithm. Statistical Energy Analysis (S.E.A.), which is a natural extension of the Power Input Method, is used to evaluate coupling loss factors for two sets of plates, one set joined along a line and the other set joined at a point. Two alternative coupling loss factor estimation algorithms are studied, one using individual plate loss factor estimations, and the other using the loss factors of the plates estimated when the plates are coupled. The modal parameters (modal density and coupling loss factors) for both sets of plates are estimated experimentally and are compared with theoretical results. The estimations show reasonable agreement between agreement and theory that is, within 5 % for the damped system of plates. For the undamped system of plates the results are less accurate with deviations of more than 100% at low modal density and approximately 30% variation at higher frequencies.