Analysis and Experimental Validation of an Optimized Gradient-Index Phononic-Crystal Lens

We propose, analyze, and experimentally verify an optimized gradient-index (GRIN) phononic-crystal lens (PCL) for increased focusing efficiency. The proposed GRIN PCL is formed from a nonsquare lattice of void inclusions in a host plate with transverse variations of the inclusion diameters. With use of a Bloch-based multiple-scattering approach, the refractive index of the lens is made to satisfy a sech profile for flexural waves and then optimized for enhanced harvesting. Under harmonic-plane-wave excitation, the resulting wavefield is analyzed with a ray approximation to characterize the focal points of the lens, followed by representative experiments that demonstrate the validity and effectiveness of the optimized GRIN structure. Furthermore, a piezoelectric energy harvester, located at the first focus of the GRIN PCL, is used to illustrate increases in power gain compared with baseline harvesting.