Low-frequency band gap characteristics of two-dimensional hollow scatterer phonon crystal plate and its formation mechanism

By using the finite element method,the characteristics of the low frequency band gap of the phononic crystal plate which is composed of hollow lead cylinder coated with silicone rubber and embedded in four epoxy resin short connecting plates are studied.The energy band structure,transmission loss and displacement field were analyzed.Compared with three kinds of traditional phononic crystal plates,which are square plate adhesion structure,embedded structure and thin plate adhesion structure,the model has more and wider band gaps in the low frequency range,indicating that the phononic crystal plates with cladding layers and short cladding plates are more likely to generate low frequency broadband.The vibration modes of the displacement vector field and the spring mass model are observed to explain the mechanism of bandgap formation.By discussing the influence of the width of the joint plate,the inner and outer radius and height of the scatterer on the first complete bandgap,it is found that the narrower the width of the connection plate,the smaller the thickness,the smaller the radius of the scatterer,the larger the outer radius and the higher the height,and the better the band gap expansion.