Inverse design of a topological phononic beam with interface modes

Inspired by the idea of topological mechanics and geometric phase, the topological phononic beam governed by topological invariants has seen growing research interest due to generation of a topologically protected interface state that can be characterized by geometric Zak phase. The interface mode has maximum amount of wave energy concentration at the interface of topologically variant beams with minimal losses and decaying wave energy fields away from it. The present study has developed a deep learning based autoencoder (AE) to inversely design topological phononic beam with invariants. By applying the transfer matrix method, a rigorous analytical model is developed to solve the wave dispersion relation for longitudinal and bending elastic waves. By determining the phase of the reflected wave, the geometric Zak phase is determined. The developed analytical models are used for input data generation to train the AE. Upon successful training, the network prediction is validated by finite element numerical simulations and experimental test on the manufactured prototype. The developed AE successfully predicts the interface modes for the combination of topologically variant phononic beams. The study findings may provide a new perspective for the inverse design of metamaterial beam and plate structures in solid and computational mechanics. The work is a step towards deep learning networks suitable for the inverse design of phononic crystals and metamaterials enabling design optimization and performance enhancements.