Flexural waves focusing through shunted piezoelectric patches

In this paper, we designed and analyzed a piezo-lens to focus flexural waves in thin plates. The piezo-lens is comprised of a host plate and piezoelectric arrays bonded on the surfaces of the plate. The piezoelectric patches are shunted with negative capacitance circuits. The effective refractive indexes inside the piezo-lens are designed to fit a hyperbolic secant distribution by tuning the negative capacitance values. A homogenized model of a piezo-mechanical system is adopted in the designing process of the piezo-lens. The wave focusing effect is studied by the finite element method. Numerical results show that the piezo-lens can focus flexural waves by bending their trajectories, and is effective in a large frequency band. The piezo-lens has the ability to focus flexural waves at different locations by tuning the shunting negative capacitance values. The piezo-lens is shown to be effective for flexural waves generated by different types of sources.