Study On Low-frequency Band Gap Characteristics And Tunability Of A Novel Two-dimensional Phonon Crystal Based On A Hollow Scatterer

Phononic crystal is a new kind of periodic composite structure.The interaction between elastic wave and periodic structure makes it impossible for waves in a certain frequency band to continue to propagate in phononic crystal.This frequency band is called band gap.The band gap characteristics make phononic crystal have broad application prospects in noise reduction,filter,acoustic waveguide and other fields.When the piezoelectric material is introduced into the phononic crystal,the incoming elastic wave and electromagnetic wave are coupled with each other to form a piezoelectric phononic crystal with electromechanical coupling effect.Compared with conventional phononic crystals,piezoelectric phononic crystals can achieve active band gap regulation.A new two-dimensional phononic crystal structure with silicone rubber as the coating,epoxy resin as the connecting plate and hollow lead column as the scatterer is designed.The equivalent spring mass model is introduced to analyze the forming mechanism of the band gap,and the strain energy is introduced to calculate the characteristic frequency,so as to verify the band structure calculated by the finite element method.In order to realize the active control of acoustic waveguide,piezoelectric materials are introduced into a newly designed phononic crystal plate.Compared with the two-dimensional conventional phononic crystal without the connecting plate structure,the newly designed phononic crystal structure obtained several complete band gaps in the frequency range below 1000 Hz.The first complete band gap is the widest,and the frequency band of the first complete band gap boundary is only affected by the mass of the oscillator and the equivalent stiffness of the spring.The scatterer and the connecting plate do not have vibration coupling at the band gap boundary.Such independent vibration is more conducive to the regulation of the band gap.Based on the vibration mode of the first complete bandgap boundary,the effects of the inner and outer half of the scatterer,the height of the scatterer and the width of the connecting plate on the upper and lower edges of the first complete bandgap are compared and analyzed.By introducing piezoelectric functional materials into the new structure,the width and position of some band gaps can be actively adjusted and adjusted by changing the electrical boundary conditions of the piezoelectric materials.Because the newly designed phononic crystal model is a phononic crystal plate with a hollow scatterer,the influence of the radius of the scatterer on the band gap is calculated.The new piezoelectric phononic crystal is used to form the supercell structure.When the point and line defect states caused by the absence of electrical boundary in the supercell structure can lead to the defect frequency band in the energy band structure,the active control of the acoustic waveguide can be realized.The new two-dimensional phononic crystal plate of hollow scatterer designed in this paper has good low-frequency characteristics,and can provide theoretical basis for noise reduction within the low-frequency range.The structure of hollow scatterer can reduce the quality of the entire crystal plate,which is beneficial to engineering applications while saving costs.The introduction of piezoelectric functional materials makes it possible to actively control the width and position of the band gap and the acoustic waveguide.