Time domain response of a piezoelectric layer

A number of one-dimensional models have been developed to inform the design of piezoelectric transducers. The majority of these models are in the frequency domain. In this paper, we develop a one-dimensional time-domain model for the mechanical response of a piezoelectric layer. Secondary effects, resulting from feedback between the acoustic and electric variables, are included in the model. Our approach utilizes Green's function for the Helmholtz equation with radiation boundary conditions and the methods of complex analysis. The model predictions are validated by comparison with a finite-difference time-domain numerical simulation of the governing acoustic equations in and outside the layer. This time-domain model enables efficient calculation of the secondary piezoelectric action effects and provides the mechanical response to an arbitrary electrical source.