Modal Analysis of a Vibrating Plate Considering Internal Damping and Application to the Estimation of Radiated Sound Power. 1st Report, Derivation of the Relationship between Total Loss Factor and Frequency at the Natural Modes of Flexural Vibration.

Abstract

The authors have proposed a basic theory for precisely estimating the frequency response of sound power radiating from plates due to their flexural vibration. In this theory, the equivalent viscous damping ratios of all the natural modes of flexural vibration are required to calculate total loss factor, radiation loss factor and driving point mobility, which are the three most important parameters for the estimation. At present the equivalent damping ratios are only determined using the experimental modal analysis of plates. However, if the damping ratios can be estimated by means of a theoretical method, the radiated sound power may be completely estimated by calculation. As the basis for that, the internal damping of metal is assumed to be viscous damping and is incorporated into the equation of flexural vibration of plates ; then, the relationship between the internal damping and the natural frequency of flexural vibration is derived using Mindlin's thick plate theory.