Flexural wave manipulation in perforated metamaterial plates with acoustic black holes interconnected by piezoelectric studs

Abstract

Aiming at achieving lower and broader bandgaps (BGs) and stronger collimation effect, this research proposes a novel perforated metamaterial plate with acoustic black holes (ABHs) interconnected by piezoelectric studs for flexural wave manipulation. Based on the differential quadrature element method together with the first-order shear deformation plate theory, the governing equations of the metamaterial plate are derived. The proposed model is validated by comparing with finite element simulation results. Finally, the wave propagation characteristics including the BGs, equi-frequency contours (EFCs), and group velocities are obtained. The results reveal that the introduction of the stud embedded with piezoelectric patches brings wider complete BGs and stronger collimation effect at lower frequencies. The boundary frequencies and bandwidth of BGs and the preferential direction of wave energy flow are tunable by adjusting geometry parameters of the unit cell. The balance between ABH and piezoelectric effects should be kept to enhance the collimation by generating the caustic lobes. Utilizing the BG and self-collimation mechanism, flexural wave propagation can be manipulated by creating point or line defects in the metamaterial plates. This research provides guidance on the design of metamaterial structure with ABHs and piezoelectric material to achieve broadband vibration absorption and directional wave propagation.