Pneumatic soft acoustic metamaterials (PSAMs) have gradually attracted attention inspired by pneumatic soft robots. Related researches show that PSAMs have significant advantages for tuning bandgaps and undergoing reversible large deformations. Most of the designed PSAMs are focus on the combination of acoustic metamaterials with different structures and pneumatic actuation based on heuristic strategies. To improve the performance of these PSAMs, topology optimization may be a powerful design tool. However, the difficulty of the design arises from the presence of material and geometrical nonlinearities coupled with the energy band performance. 

This work presents an effective topology optimization method to realize tunable bandgap designs of PSAMs. To construct contour curve with the sufficient smoothness and continuity, non-uniform rational B-splines (NURBS) method is used to design soft inflatable rubber cavity geometry. In addition, a post-processing technique is designed to address the issue of small features in the local area of optimized topologies causing non-convergence of the finite element analysis. Based on the NURBS method, the topology optimization model with a small number of design variables is defined as maximizing the bandgaps of PSAMs before and/or after inflation. The optimization problem is then solved by genetic algorithm, which eliminates the need for the complex sensitivity analysis. The comprehensive investigation of the initial designs, control points, and the post-processing techniques is performed. Numerical examples show that the proposed method provides an effective way to design PSAMs with rapid tunability of bandgaps and appropriate parameter selection can significantly improve the tunability of PSAMs.

Chen Ning, Ph.D., is a professor at Hunan University. He obtained his doctoral degrees from Hunan University in 2017, and completed a joint doctoral program at University of Michigan, Ann Arbor. His main research interests include dynamic modeling, simulation and optimization design of metamaterials systems, machine learning methods and their applications. He has led multiple research projects, including one sub-projects from the National Key Research and Development Program of China, one grant from the Advanced Materials-National Science and Technology Major Project, two grants from the National Natural Science Foundation of China (General/Youth Program), two grant from the Hunan Provincial Natural Science Foundation (General/Youth Program). As the first or corresponding author, he has published over 40 papers in SCI-indexed journals.