Modeling the hollow cylindrical piezo-ceramics with axial polarization using equivalent electro-mechanical admittance matrix

Modeling a piezo-ceramics as an electro-mechanical element is usually done using the laws of electricity. Due to complexity of the derived circuits, this kind of modeling usually results in some simplifications. In this paper using the force–velocity boundary conditions and equalizing the mechanical elements to the electrical ones, the governing equations of a hollow cylindrical piezo-ceramics with axial polarization are solved. Then the equivalent electro-mechanical impedance is represented via matrix notation. Using the matrix algebra the resonance and anti-resonance frequencies are calculated and then compared to the experimental results. The proposed method does not need to any simplification in circuit analysis, and provides the capability of modeling the various layers of piezo-ceramics and metals together in electro-acoustical transducers.