Modal analysis of the electromechanical conversion in piezoelectric ceramic soherical shells

The current study considers piezoelectric ceramic electromechanical transducers utilizing axisymmetric vibrations of complete and incomplete spherical shells. Analysis is focused on generating the modes of vibration that can be employed in the design of multimode unidirectional electroacoustic transducers for underwater applications and on determining the electrode configurations that achieve optimal electromechanical coupling for the different modes of vibration considered. Analytical expressions are presented for the modal and intermodal equivalent parameters characterizing the energy state of the shell vibration. Results of calculation and experimental verification of the resonance frequencies and effective coupling coefficients for different modes of vibration of the complete and incomplete spherical shells are in good agreement.