Research on bending vibration characteristics of phononic crystal plates based on Mindlin’s piezoelectric plate theory

Abstract

Based on Mindlin’s theory and the plane wave expansion method, the formulas are proposed for the governing equations and dispersion relations of bending waves in piezoelectric phononic crystal plates. The shear correction factors can be obtained through transcendental equations based on forced vibrations of the plate. The plates are made of inclusions of different shapes and lattice types, finding that the inclusion shape dramatically affects the mid-to-high frequency band gaps. Piezoelectric materials exhibit distinct eigenfrequencies at the high-symmetry point Γ at low frequencies. Thickness affects the band gap width differently than in two-dimensional models, and cuts influence band gap width significantly.