Analytic modelling of thickness modes in 2-2 composite transducers

We propose an analytical study of vibration modes in 2-2 piezocomposite plates. We establish separately the asymptotic dispersion equation for small lateral wavenumbers in each ceramic and polymer phase. The boundary conditions on the larger surfaces of plate are fully taken into account in a first step while continuity conditions at the interface between both phases are approximately satisfied in a second step, by means of a variational principle. Results provided by the model include frequencies, mechanical displacement and potential as functions of the geometry and material properties of piezocomposite. We give a comparison with experiments on composite samples with constant pitch and various thickness