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The influence of coupling between flexural and extensional deformation and coupling between structure and acoustic volume on the dynamic response of piezoelectric ceramic transducer elements mounted on metal diaphragms is analyzed using three analytical methods: 1) classical boundary value techniques; 2) simple direct variational procedures; and 3) finite element methods. The analyses are able to predict the voltage output of the transducer, including resonant amplitudes and shapes, with reasonable accuracy and also to indicate critical front and back acoustic volume design parameters needed to control resonance. The finite element model includes a general formulation for axisymmetric layered shells of revolution (which degenerates to a circular plate), whose average normal displacement is coupled to the long wavelength motion of air in adjacent cavities (acoustic stiffness), ports (acoustic mass), and porous plugs (acoustic damping). The methods outlined here are also applicable to window-enclosure response to sonic boom excitation, skull-brain impact studies, and the study of respiratory mechanics.