Control of low-frequency Lamb wave propagation in plates by boundary condition manipulation

Abstract

Locally resonant metasurfaces can control the propagation of Lamb wave modes in a plate. The resonator is typically designed through frequency matching: adjusting its geometry and/or materials properties by trial and error until its resonance frequency matches the frequency of the target Lamb wave mode. We demonstrate that although frequency matching appears effective for controlling the A0 wave mode, it may fail in the case of the S0 mode. This paper proposes a fundamentally different approach to design a specific metasurface to forbid the propagation of a prescribed Lamb wave mode in a plate. The proposed approach is based upon manipulating the boundary conditions on the top surface of the plate. Different types of Cauchy boundary conditions applied to the surface are shown to control the reflections and mode conversions of low-frequency A0 and S0 Lamb waves. Even a small patch with the modified boundary conditions can be effective. Finally, we show that a local “clamping” resonator that assimilates Cauchy boundary conditions on the surface of the plate changes the plate dispersion characteristics resulting in mode conversion and reflection. This finding provides a rational procedure to design a specific metasurface. The surface-mounted resonators enable control of wave propagation in plates without compromising structural integrity, are easily installed, and can be retrofit to the existing planar structures. The numerical results agree well with the experimental results reported in the literature.