Study of ultrasonic waves propagation in 1D piezoelectric tunable phononic crystals

Résumé

This work deals with the numerical study related to the acoustic waves propagation in a one-dimensional (1D) piezoelectric phononic crystal (PPC) constituted of a periodic pattern made of two perfectly glued materials: one piezoelectric (active), the other elastic (passive). The study is interested in the tunability of piezoelectric inclusions in order to control the ultrasonic waves propagation in MHz frequency range, from an external nonlinear electrical component connected to the terminals of the piezoelectric elements. The considered active inclusions are the seat of an electromechanical coupling obtained by connecting the PPC to a diode or a memristor. After modeling the dynamic resistance of the electronic devise and evaluating the effective properties of the piezoelectric plate, based on the piezoelectricity equations, a 1D analytical model is proposed to take into account the resistive impedance effect connected to the electrodes of the active plate. Thus, it has been shown that the application of various electrical boundary conditions (EBCs), enables to change the effective properties of the piezoelectric plate in particular and those of the PPC in general. Consequently, the bande structure of the acoustic transmission can be modulated. Elastic waves dispersion is then electrically tuned, leading to a significant variation of the forbidden band or bandwidth position in the dispersion diagrams. Depending on the applied EBCs, it has been numerically demonstrated the possibility of opening Bragg or hybridization gaps in the PPC band structure.

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