Vol. 15, No. 1, 2020

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Analytical modeling and computational analysis on topological properties of 1-D phononic crystals in elastic media

Muhammad and C. W. Lim

Vol. 15 (2020), No. 1, 15–35
Abstract

The topological interface state governed by topological phononic crystals (PnC) can potentially host one-way, backscattering free nontrivial edge modes, immune to defects and sharp edges. We study here 1D topological phononic crystals with interface modes/states generated by an exchange of wave mode polarization and geometric phases, using the spectral element method with Timoshenko beam model for flexural wave propagation. The constitutive relations for the longitudinal wave, and modeling and formulation are derived for theoretical band structure and frequency response studies. The analysis is validated by finite element numerical simulations. The geometric phases of the Bloch bands are determined by numerical Zak phase analysis. As the geometric properties of the PnC vary, a band transition resulting from an exchange in wave mode polarization is observed and the symmetry characteristics of the Bloch bands are determined. The geometric phases provide useful information about the interface mode that is generated when the mode transition frequency is common between the bandgaps of topological PnC. We further conduct theoretical and numerical studies on the presence of interface state and excellent agreement observed between both models is reported. The theoretical details of the topological PnC with protected interface mode can be helpful for better understating of research in phononic crystals.

Keywords
geometric phase, interface mode, spectral element, topological phononic crystals, Zak phase
Milestones
Received: 29 July 2019
Revised: 7 November 2019
Accepted: 29 November 2019
Published: 7 January 2020
Authors
Muhammad
City University of Hong Kong Shenzhen Research Institute
Shenzhen 518057
China
C. W. Lim
Department of Architecture and Civil Engineering
Kowloon, Hong Kong SAR
China