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An axisymmetric analytical model is presented of axially polarized piezoelectric ceramic rings with radius a few times the wall-thickness and the length. The only assumptions made are that axial displacement and electric potential are functions of only the axial coordinate and that radial displacement is a function of only the radial coordinate. Then, exact solutions to the exact governing equations are determined. The boundary conditions on electric potential are satisfied exactly. The other boundary conditions are satisfied in an average sense. The input electrical admittance of stress-free rings with losses are computed and compared with that obtained using ATILA—a finite element program. Good agreement is obtained for the resonance and anti-resonance frequencies and the values of conductance and susceptance at the first resonances in the lower and upper branches.
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Acknowledgment
The authors thank Director, NPOL for permission to publish this work.
Paper originally presented at AMF-4, Bangalore, India, December 12-15, 2003.