Subwavelength negative refraction and flexural wave lens design via resonant double-negative piezoelectric metamaterial

We report the concept and demonstration of a double-negative, resonant metamaterial characterized by both dynamic negative mass and stiffness for negative refraction of flexural wave modes by means of a lens designed using this concept. The negative equivalent material properties are obtained in the subwavelength regime by concurrently exploiting both the effect of mechanical resonators (negative mass) and of piezoelectric patches with inductive resonant shunts (negative stiffness), leading to double-negative behavior. Following the theoretical foundations based on a modal framework, we analytically derive the frequency-dependent mass and stiffness properties as a function of the electromechanical parameters. The findings are corroborated by numerical computation of dispersion properties and simulations showing the focusing of a point source. As a case study, energy harvesting performance enhancement by exploiting the piezoelectric effect at the focal spot is also discussed.