Topology optimization design of metasurfaces to control Lamb wave propagation

Abstract

Metasurfaces are engineered metamaterials with a structured surface used in electromagnetics, optics, elastodynamics, and acoustics. Elastodynamic metasurfaces can control plate or surface waves. Wave control using metasurfaces has applications across length scales from designing electronics to vibration control systems. Previous works have approached the design of metasurfaces through experimentation and parameter-tuned designs, but no systematic design methodology has been proposed yet. This work addresses the design of resonant metasurfaces to forbid the propagation of plate waves. This is achieved through designing the local resonators using a density-based topology optimization method. Specifically, we design resonators that at their base, fulfill a set of continuity conditions. These are equivalent to boundary conditions mathematically proven to provide reflection and mode conversion for Lamb or Rayleigh waves. Thus, the optimization problem is defined as the minimization of a weighted sum of the displacements and stresses that define such boundary conditions. A topology optimization algorithm is developed that includes material interpolation models, penalization schemes, filtering techniques, sensitivity analysis, and solution methods. A complex scheme integrating the density-based mathematical parametrization, finite element models, data processing modules, optimization solvers, and 3D structural visualization is implemented