Asymptotic Formulae for the Acoustic Self-Impedance of Simply-Supported and Simply Supported-Clamped Annular Plates

This study focuses on the sound radiation of a vibrating flat annular plate. The rigorous theoretical considerations deal with sometime-harmonic and axisymmetric vibrations. Three different boundary configurations are considered, i.e. one of the plate’s edges is simply supported and the other one is clamped or also is simply supported. The active and reactive self-impedance of the system are presented in their Hankel’s representations, valid within the whole frequency spectrum. The expressions obtained are transformed to their elementary forms, valid for the high frequencies. Low fluid loading and low internal friction of the plate are assumed. The obtained results are illustrated with sample plots in the domain of acoustic wavenumber. Elementary formulae presented can be useful for further theoretical analysis of the total sound power radiated by an excited flat plate in an acoustic fluid as well as for efficient engineering computations.