On the method of extraction of lumped parameters for the radiation impedance of complex radiator geometries

This work addresses the problem of finding expressions for the radiation impedance of a circular plate with cuts (holes + slits) and mounted in an infinite baffle. Due to the nontrivial nature of the structural geometry and the boundary conditions, analytical solution of the required Rayleigh integral is difficult for this case. The analysis in this case is carried out numerically using COMSOL Multiphysics. The air on top in contact with the vibrating plate, loads the plate with additional mass and also dissipates away energy depending on the frequency of vibration. The numerical solution obtained using FEA needs to be converted into suitable frequency based expressions. We use curve fitting to relate these radiation impedance values to an already reported equivalent circuit (for modeling the radiation impedance) in the literature. The detailed method of lumped parameter extraction, as well as the method of reduction of the circuit to its high and low frequency counterparts, is reported in this paper. The method described here is a generic one and can be used for any kind of geometry.