Flexural wave band gaps of sonic black hole beams based on the plane wave expansion method

Abstract

To further improve the damping capacity of structures, research on new damping structures has become an inevitable trend. As a continuous power-law transformation cross-section structure, sonic black holes can suppress the propagation of bending waves in damping structures. A one-dimensional photonic crystal beam with a sonic black hole as its primitive cell is constructed to extend the damping frequency band of the sonic black hole by combining the periodic structures in photonic crystals and the sonic black hole. Based on the Bernoulli-Euler beam theory, the plane wave expansion method is derived to calculate the bending wave band gaps of the beam, and the convergence of this method is analyzed. The transfer matrix method is used to verify the results, which proves the correctness of the derivation process and the feasibility of calculating the band gap of the periodic black hole structure via the plane wave expansion method. The influence of changes in the parameters of black hole materials on band gaps characteristics is analyzed. The results show that choosing a material with a small longitudinal wave velocity to form a periodic black hole beam can obtain a low-frequency band gap and that adjusting the difference in material properties can obtain a wide-frequency band gap.