Band Gap Design of Beam-Supported Phononic Crystal by Regulation and Control of Beam Bending Stiffness

PurposeBending stiffness is an important physical parameter of beam determining the band gap (BG) characteristics for beam-supported phononic crystal (PnCs). To reveal the role of bending stiffness on PnCs design, two-component PnCs is designed in which a solid mass block serves as scatterer and beams are used to connect the scatterer with the matrix.MethodFinite element method was used to obtain the BG characteristics for the designed beam-supported PnCs. Different cross sections are designed with different bending stiffness for vibration control in wave transmissions.ResultsThe BG width of I-shaped beam-supported PnCs is wider than rectangular section, cross-shaped section, box section, and H-shaped section. Compared with rectangular section beam-supported PnCs, the bending stiffness of the I-section beam in y direction and z direction decreases by 34.4% and 75.5%. The I-shaped beam-supported PnCs reveal two BGs due to lower bending stiffness. One is 4.2 kHz, and the other is 12.3 kHz. The center frequency of the first band gap is 17.2 kHz and the second is 34.4 kHz. The effects of the elastic modulus and density of the material on the bending stiffness and the band gap characteristic in the unit cell are further discussed.ConclusionThe geometry of the cross section, the elastic modulus and the density of material can be used to design the bending stiffness. The BG characteristics can be designed by the regulation and control of the bending stiffness in beam-supported PnCs.