Design optimization of metamaterials to control waves in cylindrical rods

Abstract

Metamaterials can control different modes of waves by tuning their bandgap structures. Various design strategies are implemented to obtain desired responses of metamaterials by solving multiple forward problems using parametric sweeps, topology, and shape optimization problems. This study focuses on the design of cylindrical metamaterials to control wave propagation in a cylindrical rod using a shape optimization approach. Topology optimization requires relatively more computational resources and time as well as it also gives relatively complex structures in comparison with shape optimization. Optimal widths of layered elastic materials arranged periodically along an axis, on subsurface, and an outer surface of cylindrical surface are obtained by solving multiple time-dependent shape optimization problems. Optimization problems are solved using the finite element method and non-gradient optimization algorithm. Single and multi-objective functions are defined to reduce only axial and both axial as well as radial displacements integrated over the end surface, and monochromatic Gaussian input pulse is considered in this study. Every design solution obtained during each design iteration can be easily manufactured as a weak constraint is applied to the total length of the metamaterial. Prior knowledge of possible bandgaps helps to set an effective optimization problem, but it is not a necessary condition.