Topological Edge State of Lamb Waves in Pillared Phononic Crystal Plates

Abstract

The Hall effect of elastic waves has attracted much attention due to its unique properties. A hexagonal lattice phononic crystal plate model is designed in this paper. By changing the spatial symmetry of the unit cell, a band gap for the A₀ Lamb wave is opened. The existence of the edge state of the phononic crystal plate is obtained by finite element simulation. It is found that both zigzag-type edge and bridge edge are topological edge states by analysis of the band structure of the supercell. A rectangular model with a straight channel is designed and the simulation results show that the two types of channels are topologically protected only for the A₀ mode Lamb wave but not for the S₀ mode. In addition, the results of numerical simulation are verified by experimental data measured by a laser vibrometer. Finally, it is found that neither upside V-shaped channels nor channels with defects will affect the stable propagation of A₀ Lamb waves along the proposed route. This proposed model and method are helpful in broadening the means of regulating elastic waves in phononic crystal structures, and extending practical application of topological edge states in such structures.