Willis elastic metasurfaces for unidirectional manipulation of flexural waves

Abstract

Exceptional points label the region of the parameter space of a system in which two or more eigenvalues of a non-Hermitian Hamiltonian and their associated eigenvectors coalesce and become degenerate. Owing to the rich physics and engineering potential, there has been a recent interest in developing such acoustic or elastic media that display exceptional points. In this work, we present the design of a non-Hermitian planar elastics metasurface exhibiting Willis coupling for the control of flexural waves. The metasurface contains a series of unit cells with asymmetrically loaded piezoelectric and metallic blocks. Loss is further added to the system by negative capacitance piezoelectric shunting, which leads to zero reflection from one side of the metasurface. Asymmetric reflection properties are achieved when approaching the exceptional point of the system. Numerical simulations show that the proposed metasurface can realize asymmetric modulation of flexural waves propagation on the beam, manifested by unidirectional focusing of the incident waves. The proposed elastic metasurface has a planar profile, and the amount of loss can be conveniently tuned by the shunted piezo, making it useful for the manipulation of flexural waves where asymmetric control is desired.