Analysis of wave band gaps in mechanical metamaterial based on Nelder–Mead method

Abstract

One of the fundamental challenges in engineering design of an elastic metamaterial is optimizing its structure in a fine but controllable geometry based on a performance criterion. In this study, the wave manipulation ability of the metamaterial is taken as the key criterion for the optimization of its unity structure governed by the changing geometric parameters. The complete dispersion relationship of the metamaterial is set as the performance criterion which is acquired by scanning the wave vector k along the contour of the irreducible Brillouin zone in the reciprocal space for the unit cell and evaluating its eigenfrequency values in different eigenmodes. For the optimization algorithm, the Nelder–Mead method is programmed in the form of MatLab scripts incorporated with tailored parameter ranges to ensure geometric compatibility and a finite element analysis (FEA) solver for eigenfrequency evaluation. Parametric optimization is conducted for 100 iterations where promising convergence is observed. The optimized geometry is then compared to the initial in its performance. In all three case studies, including planar and spatial lattices, the optimized geometry showed superior properties and larger complete band gaps. The Nelder–Mead method is proved to be an effective tool for metamaterial optimization.