A theoretical model is presented for the analysis of an asymmetrical piezoelectric annular bimorph (APAB) in dynamic harmonic motion. The APAB is assumed to be so thin that the thickness dependent stresses vanish throughout. The conjugate parameters of the admittance and impedance matrices are derived using the variational principle. Both the extensional and flexural motions are considered in deriving the motional equations and the boundary conditions. By using the symmetry characteristic of the admittance matrix, the derivation procedure for the impedance and admittance matrices is thus greatly simplified. The resonance and antiresonance frequencies and the effective electormechanical coupling factors are calculated using the matrices. These present methods are applied to three special cases: a single piezoelectric ring in extensional motion, a triple-layer APAB in series or parallel connection, and a triple-layer APAB with sensor and actuator. The results are compared with previous publication and finite element methods, and it is found that the present methods are very effective in analyzing the piezoelectric multilayer annular transducers.
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