Electro-mechanical admittance matrix for modeling axial polarized cylindrical piezo-electrics

The equivalent electro-mechanical admittance matrix of cylindrical piezo-electrics with axial polarization was derived, and based on the electrical terms of this matrix, the resonant and anti-resonant frequencies of the cylindrical piezo-electrics were obtained. Then, these results were compared with the obtained experimental values of resonant and anti-resonant frequencies. The obtained results show an average erorr 2 % for resonant and 5 % for anti-resonant frequencies, which have good precision and matching. In this method, the cylindrical piezo-electric was modeled by using the force-velocity boundary conditions and equalizing the mechanical elements with the electrical ones. The force-velocity equalizing provides the anti-resonant frequency of the unit, which is required to design the piezo-electric transducers for sensing applications. This method is useful for modeling piezo-electric transducers composed of several stacks of cylindrical shaped piezo-electrics in both longitudinal and flexural stimulation types. The expression in matrix notation provides a simple way for modeling and analyzing multilayered piezo-electric transducers compared to the analytical method and the finite element analysis with more pricision and lower time and cost-consumption, respectively.