Deep learning-based design of ternary metamaterials for isolating full-mode waves

Abstract

A deep learning-based methodology is presented to design the topologies and periodic constants of ternary metamaterials under different site conditions, considering both in-plane and anti-plane waves (full-mode waves) coming together. A variational autoencoder (VAE) and a series–parallel neural network (SPNN) are constructed, based on which the design model is established and the metamaterial customization is realized. One thousand designs are performed, where the determination coefficient reaches 0.982, the root mean square error is only 0.785, and the mean design error is 3.1%, evaluating the accuracy and stability of the deep learning method. To illustrate the generality of the presented method, metamaterials under different site conditions are designed. For the same target, multiple sets of metamaterials are given, which reflects the non-uniqueness of design problems. Two sets of metamaterials respectively for two practical examples are customized and discussed with 3D finite element models, verifying their ability of isolating vibrations in all directions.