The Approximate, High Frequency Response of a Panel With Attached Masses

Abstract

The high frequency response of a panel with attached masses is approximated using transient, asymptotic modal analysis (AMA). These relations are derived by applying asymptotic simplifications to classical solutions in both the time and frequency domains. The geometry consists of several masses that are attached to a panel to which impulsive excitations are applied. Predictions are made of the mean-squared, transverse displacement history and the localized responses near the added masses. These are compared to classical solutions and it is shown that for a few masses that are separated by more than a mean wavelength, the panel behavior can be estimated well by the AMA expressions. The approximate solutions are shown to require less than 20% of the computational time and memory of the classical solutions and are applicable to general forms of excitation. The resulting capability can be used to estimate acoustic emissions from vibrating equipment and to model structure-borne sound and its effects on sensitive equipment.