Session: VIB-03-03: Dynamics & Waves in Solids and Metamaterials III

Paper Number: 97712

97712 - Conformal Gradient Index Phononic Crystal Lens Design for Elastic Wave Focusing in Curved Structures 

In recent years, phononic crystals and metamaterials have been proven very effective for elastic wave focusing. They are artificially engineered periodic structures that consist of periodic arrangement of inclusions over a base structure. A special class of phononic crystals, called Gradient Index Phononic Crystal (GRIN-PC) lenses, are able to focus elastic waves due to gradient distribution of refractive index. The gradient refractive index within the phononic crystal structure is achieved with gradual spatial variation of geometric and/or material properties of periodically placed inclusions over a base structure. The GRIN-PC lens concept has been previously implemented over planar structures using GRIN lens theory from optics. Whereas it was not explored before for curved structures until recently the author demonstrated a conformal GRIN-PC lens design implemented over a steel pipe. However, the design was specific to a pipe geometry and the focal locations were determined approximately using planar GRIN lens theory. In this work, we are developing a generalized framework for GRIN-PC lens design that can be implemented over any curved surface effectively focusing elastic wave energy at a desired spot. As opposed to homogeneous base structures, the PC lens is generally anisotropic resulting in directional dependence of refractive index. Moreover, for different inclusions, the anisotropy of the crystal is different and thus a simple GRIN theory is not sufficient to describe the wave trajectory and focal locations within the GRIN-PC lens. In order to validate the focal regions of GRIN-PC lens implemented over a steel pipe, we obtained polynomial fits to equal frequency contours for determining the wave speed along different directions in each unit cell and used Snell's law to trace the ray trajectories in the lens region. The focal region obtained from intersection of analytical ray trajectories at the lens centerline matched very well with the high intensity region in the numerical simulations for multiple pipe modes. In order to extend this analysis to a generalized curved structure, we consider each unit cell locally to evaluate its dispersion characteristics. After mapping the unit cells on the structure, the dimensions/material properties of inclusions in each unit cell are set so as to follow hyperbolic secant distribution of refractive index transverse to the wave propagation direction. Once the refractive index distribution is known, the ray trajectories inside the lens can be traced using Snell’s law to determine the focal region.

Presenting Author: Hrishikesh Danawe University of Michigan

Presenting Author Biography: Hrishikesh is a PhD candidate in Mechanical Engineering at University of Michigan. He joined the ME doctoral program in Fall 2019. His broad area of research interest is dynamics and vibrations. He is particularly interested to work in the emerging field of mechanical smart structures and architectured metamaterials. His doctoral research is advised by Dr. Serife Tol and it is focused on designing novel metamaterial and phononic crystal based conformal elastic lenses for elastic wave focusing in civil and mechanical structures. Hrishikesh received his Bachelors and Masters (Dual) degree in Mechanical Engineering from Indian Institute of Technology, Kharagpur, India.

Authors:

Hrishikesh Danawe University of Michigan
Didem Ozevin University of Illinois at Chicago
Serife Tol University of Michigan