Wave propagation and attenuation in plates with periodic arrays of shunted piezo-patches

Periodic arrays of shunted piezoelectric patches are employed to control the wave propagation in a thin plate. The performance is characterized through the application of finite element method and Bloch theorem. This article proposes an effective approach to gain the dispersion properties of the periodically shunted plate in any directions from the solutions of transcendental eigenvalue problems. The results show that resistive shunts can tune the location and attenuation constants of the Bragg gap, while the internal resonances of resonant shunting system split the dispersion curves and form a locally resonant band gap. Moreover, the Bragg gap is directional, whose width varies enormously with directions. However, the locally resonant gap almost keeps the same in different directions, i.e., the gap is complete. Also, the influences of different shunting parameters to the band gaps are investigated in detail.