Asymptotic formulae for the acoustic power output of a simply-supported circular plate

Computations of standardized active and reactive sound power for a simply-supported circular plate have been investigated. The plate's vibrations are axisymmetric and time-harmonic. The Kirchhoff-Love model of a perfectly elastic plate has been used. The plate is embedded in a planar and rigid baffle. Integral formulae for the active and reactive sound power, which are valid for high frequencies, have been transformed to elementary formulae useful for numerical computations. Based on some generalized formulae some energy magnitudes for clamped as well as simply-supported circular plates have been derived. The asymptotic expressions presented herein are independent from such parameters as the plate's thickness and the density of the plate's material. However, they enable us to compute a number of suitable magnitudes for any simply-supported circular plate. The standardized sound power of the successive vibrations modes computed herein can constitute basis for the analysis of the total sound power of a forced, damped, and fluid-loaded plate, which is embedded in an infinite baffle.