Lateral resonances in 1–3 piezoelectric periodic composite: Modeling and experimental results

Abstract

The objective of this work is to provide an accurate model of the lateral resonance modes in 1–3 piezoelectric composite materials. These materials are widely used in ultrasonic transducers and the lowest lateral mode frequency gives the upper limit for the usable transducer bandwidth. Considering the propagation of purely transverse waves in a 2-D periodic medium of infinite thickness, two different approaches for obtaining the solutions are presented and compared. The first approach is based on the use of the Bloch waves theory. The second is a straightforward method (a so-called membrane method) which consists in numerically solving the propagation equation in the two-phase medium while taking into account the periodic boundary conditions. Methods based on both models are described that allow the calculation of the dispersion curves and the stop band limits, as well as the frequencies and the displacement fields of the lateral modes. A test case is used to compare and discuss the theoretical predictions provided by each model. The calculations of the first lateral mode frequency are compared with experimental values obtained for samples with different ceramic volume fractions. The conclusion reached indicates that the infinite thickness assumption is valid for plates of practical interest and that the membrane model enables the prediction of lateral mode frequency with low computation effort and an accuracy better than 5%.