Focussing bending waves via negative refraction in perforated thin plates

摘要

We propose a design of a periodically perforated thin plate leading to lensing effect of bendingnwaves via negative refraction. To achieve this goal, we first analyze the band spectrum of thenbi-harmonic operator for an array of freely vibrating square voids using both numerical u0001finitenelementsu0002 and asymptotic methods. We then find some point in the reciprocal space where thenacoustic dispersion surface displays a convex isofrequency contour shrinking with frequency. Wenfinally demonstrate that a point force generating a bending wave above a finite array of 221nperforations displays an image underneath according to the Snell–Descartes inverted laws. © 2010