Optimizing graded metamaterials via genetic algorithm to control energy transmission

Abstract

Optimization of functionally graded metamaterial arrays with a high dimensional and continuous geometric design space is cumbersome and could be accelerated via machine learning tools. Mechanical metamaterials can manipulate acoustic or ultrasonic waves by introducing significant dispersive and attenuative effects near their natural frequency. In this work, functionally graded structures are designed and optimized to combine the energy attenuation performance of multiple unit cells with varying frequency responses and to reduce the interlayer mismatch effects. Optimization through genetic algorithms avoids many local minima related to high dimensionality of the design space, but requires many iterations. A reduced order model (ROM) is applied, which can reproduce the transmission response traditionally calculated with FEM in a fraction of the time. Pairing GA and the ROM together, an array of 6 unit cells (with a total of 18 independent geometric design variables) is optimized to have stop bands with extended width and sharper boundaries. Symmetric functionally graded structures are determined to have optimal geometric configurations. Measured 3D printed features are projected onto the ROM solutions to quantify the effect of printing uncertainty on array performance. Repeatability error of ±20μm is determined to reduce the mean depth of the transmission stop band by a factor of 102 and introduce small shifts in center frequency and band width. Proposed methods to improve the resolution of accessible points in the ROM space, reduce sensitivity to geometric uncertainty, and add design freedom include introducing out-of-plane perforations and varying constituent materials using tunable filled resin systems.