Inverse Design of Linear and Nonlinear Cylindrical Metamaterial Rod

Abstract

Continuum elastic metamaterials can be used to reduce system-generated 2nd harmonics and they should also pass the fundamental harmonics during nonlinear ultrasonic testing. Linear metamaterials are designed based on the bandgap structure of the periodic layered materials showing contrast in acoustic impedances. Design parameters such as widths of the periodic layered elastic materials are calculated by a parametric sweep by solving eigenvalue problems, and the transfer matrix method. Most of the design studies assume infinitely long periodic elastic layers, but in practice length of metamaterial is limited by the reduction in fundamental amplitude of input short pulse. Though the linear metamaterials are designed for nonlinear ultrasonic applications, considering geometric and material nonlinearity of the layered elastic materials which contributes to harmonic scattering, the sensitivity of widths of layered materials to amplitudes of the 2nd harmonics, along with the linear interference is the most realistic modeling approach. In this study, linear and nonlinear metamaterials are designed using shape optimization techniques by solving transient finite element studies considering realistic geometric and material models. Gradient-free algorithms such as co-ordinate search and Nelder Mead are used during optimization. Effective design approaches are proposed and demonstrated to control longitudinal modes in a cylindrical rod.