Nearly-isotropic adjustable phononic crystal lenses using concentrated balls with Hertz contacts

Abstract

In this letter, using concentrated balls, we propose a kind of adjustable phononic crystal lenses capable of focusing A0 mode Lamb waves. Due to the small Hertz contact area between the balls and the host plate, a nearly-isotropic band structure and a nearly-circular equal frequency contour of the A0 mode Lamb waves can be obtained, which is desired for the purpose of spot-focusing. To address the configuration adjustability, we design two PCLs, the gradient-Index (GRIN) and Luneburg PCLs. Specifically, we consider PCLs with unit cells of relaxed design parameters and validate that focusing spots can still be achieved even when the refraction index profile is not perfectly matched. Although the proposed PCLs are realized and demonstrated with commercially available steel balls, the Hertz contact-based unit cells can be extended to other PCL designs using additive manufacturing technique as long as the contact area is minimized to approach Hertz contact.