Omni-directional lens for structure-borne wave focusing and energy harvesting

Abstract

In this paper, a Luneburg lens is explored for omnidirectional structure-borne wave focusing both numerically and experimentally. The proposed lens is formed by radially distributed blind holes with different diameters based on the gradient index phononic crystal theory. The radial orientation and diameter of the holes are determined according to the refractive index distribution which is guided by finite-element simulations of the lowest asymmetric mode Lamb wave band diagrams. According to this design, the wave travels slower at the center of the lens and converges at the focal spot which is on the circular lens boundary. Wave simulations are performed in COMSOL Multiphysics® under plane wave excitation from a line source and wave focusing is observed at the opposite border of the lens with respect to the incoming wave direction. Experimentally measured wave fields with a scanning laser vibrometer successfully validate simulated wave focusing. Furthermore, omnidirectionality is verified by testing the lens under plane wave excitation from different directions. With piezoelectric energy harvesters located at the boundary of the Luneburg lens substantially larger power output can be obtained as compared to the baseline case of energy harvesting without the lens on the uniform plate counterpart for the same incident plane wave excitation.