An Equivalent Circuit of Longitudinal Vibration for a Piezoelectric Structure with Losses

Equivalent circuits of piezoelectric structures such as bimorphs and unimorphs conventionally focus on the bending vibration modes. However, the longitudinal vibration modes are rarely considered even though they also play a remarkable role in piezoelectric devices. Losses, especially elastic loss in the metal substrate, are also generally neglected, which leads to discrepancies compared with experiments. In this paper, a novel equivalent circuit with four kinds of losses is proposed for a beamlike piezoelectric structure under the longitudinal vibration mode. This structure consists of a slender beam as the metal substrate, and a piezoelectric patch which covers a partial length of the beam. In this approach, first, complex numbers are used to deal with four kinds of losses—elastic loss in the metal substrate, and piezoelectric, dielectric, and elastic losses in the piezoelectric patch. Next in this approach, based on Mason’s model, a new equivalent circuit is developed. Using MATLAB, impedance curves of this structure are simulated by the equivalent circuit method. Experiments are conducted and good agreements are revealed between experiments and equivalent circuit results. It is indicated that the introduction of four losses in an equivalent circuit can increase the result accuracy considerably.