A coupled-mode theory for periodic piezoelectric composites

A coupled oscillator model to calculate the resonance spectrum of a one-dimensional piezoelectric composite plate, used in ultrasonic transducers, is proposed. Two resonant modes, one produced by the elastic wave reflection on the plate boundaries (thickness resonance) and the other by the reflection on the periodic discontinuities (lateral resonance) are considered. A Kronig-Penney model is used to calculate the lateral resonances. The thickness resonance is obtained with an effective medium model. The coupling of these two modes is described by a biquadratic equation whose solutions are the resonant frequencies of the piezoelectric composite plate. A criterion for a distribution of phases to keep the spurious lateral resonances away from the thickness resonance vicinity is obtained.