Electro-mechanical equivalent circuit for the radial vibration of the radially poled piezoelectric ceramic long tubes with arbitrary wall thickness

Based on the theory of plane strain problem, the radial vibration of the radially poled piezoelectric ceramic long tubes with arbitrary wall thickness is studied. The exact analytical theory is developed and the exact solutions for the radial displacement and the electrical potential are obtained. The three-port electro-mechanical equivalent circuit of the piezoelectric ceramic tube in radial vibration is obtained. Based on the circuit, the electric admittance is obtained and the resonance/anti-resonance frequency equations are given analytically. The relationship between the resonance/anti-resonance frequency and the geometrical dimension is analyzed. For comparison, numerical method is used to simulate the radial vibration of the piezoelectric tube. Meanwhile, some radially polarized piezoelectric ceramic tubes are designed and manufactured and the resonance/anti-resonance frequencies are measured. It is shown that the analytical resonance/anti-resonance frequencies are in good agreement with those from the numerical method.