Efficient Inverse Design of Heterogeneous Locally Resonant Elastic Metamaterials for Targeted Vibration Suppression

Locally resonant elastic metamaterials (LREM) usually constitute a periodic arrangement of unitcells, which can be tuned to potentially damp out vibration in selected frequency ranges, thus yielding desired bandgaps. However, being limited to the parameters of just one unitcell can sometimes lead to an overly constrained design space and therefore rendering many desired bandgap configurations unattainable. One hypothesized approach for increasing the design space, thereby tunability of the LREM, is to divide the finite structure in two or more zones or blocks, each composed of a unique finite structure that is therefore heteregoneous. The hypothesis behind this being that when properly placed each unitcell block helps in isolating vibrations in its bandgap, thereby insulating the rest of the structure . However, the increased search space and the analysis on the finite structure can make this concept both tedious to analyze and optimize. This paper develops a computationally-efficient invertible neural network based learning framework for accelerated design of such LREM structures. First, an Invertible Neural Network (INN) is trained to approximate the bandgap of a given unitcell and vice-versa. Subsequently, the INN is used in reverse to retrieve two unitcells corresponding to different bandgaps of interest. Then an optimization is performed to determine the arrangement of these INN retrieved unitcells in the finite structure in such a way so that the isolation locations are protected. Finaly, this framework is applied to design a 2D LREM plate for noise isolation under desired bandgap constraints. Our results show that the optimal design obtained is better as compared to a baseline design.