Investigation of Bandgap Properties of a Piezoelectric Phononic Crystal Plate Based on the PDE Module in COMSOL

Abstract

Aiming to address the vibration noise problems on ships, we constructed a piezoelectric phononic crystal (PC) plate structure model, solved the governing equations of the structure using the partial differential equations module (PDE) in the finite element softwareCOMSOL6.1, and obtained the corresponding energy band structure, transmission curves, and vibration modal diagrams. The application of this method to probe the structural properties of two-dimensional piezoelectric PCs is described in detail. The calculation results obtained using this method were compared with the structures obtained using the traditional plane wave expansion method (PWE) and the finite element method (FE). The results were found to be in perfect agreement, which verified the feasibility of this method. To safely and effectively adjust the bandgap within a reasonable voltage range, this paper explored the order of magnitude of the plate thickness, the influence of the voltage on the bandgap, and the dependence between them. It was found that the smaller the order of magnitude of the plate thickness, the smaller the order of magnitude of the band in which the bandgap was located. The magnitude of the driving voltage that made the bandgap change became smaller accordingly. The new idea of attaching the PC plate to the conventional plate structure to achieve a vibration damping effect is also briefly introduced. Finally, the effects of lattice constant, plate width, and thickness on the bandgap were investigated.

Keywords

• piezoelectric phononic crystal plate
• partial differential equation
• band structure
• vibration mode
• transmission curve