An electromechanical model for clamped-clamped beam type piezoelectric transformer

In this paper, an analytical solution of a fixed-fixed beam type piezoelectric transformer with Euler-Bernoulli beam assumption is proposed. The electromechanical equations are first derived for transient motions, and coupled expressions for the mechanical response and voltage output are obtained. The resulting equations are further reduced for the case of excitation around the first resonance frequency. Analyical solutions of mechanical response, voltage, current, and power outputs are presented. From analytical model, output voltage depends on the lengthes of two electrodes, the length of beam, and the Young´s modulus ratio and thickness ratio between PZT layer and substrate. The lengthes of input electrodes and output electrodes should be 0.22 time length of beam to achieve the largest output when the transformer is excited at first resonance frequency. The output voltages and the resonance frequencies of transformers are proportional and inversely proportional to the lengthes of beams, respectively. The combination of Young´s modului and thicknesses of PZT layer and substrate change the position of natural axis and the bending stiffness of beam, concurrently. However, output voltages of transformers depend not only on the postion of neutral axes but also on bending stiffnesses.