Study On Band Gap Characteristics Of Phononic Crystals In Tetragonal Lattice

Vibration and noise are common in daily production and life,but for the processing of some precision instruments and the military field of high precision,the requirements for vibration and noise are quite high,so vibration and noise reduction has become an important work.The structure of phononic crystal can reduce vibration and noise at the same time,and its unique band structure can prevent the elastic wave from propagating smoothly within the forbidden band.However,as far as the current research is concerned,the suppression effect of vibration noise in the high-frequency region is obvious,and there are many factors affecting the energy band curve of phononic crystal,which adds a lot of obstacles for the practical application of phonon crystal.Based on this,this paper studies the vibration and noise reduction effect of phononic crystal at low and medium frequencies,and analyzes the influence of different factors on the energy band structure of phononic crystal,and improves the structure of the original locally resonant phononic crystal.This paper mainly studies from the following aspects:(1)The basic theory of phononic crystal is introduced,and then the plane wave expansion equation of two dimensiona phononic crystal in tetragonal lattice is derived based on the model in this paper.The MATLAB program is written to select the appropriate plane wave number for the subsequent calculation of dispersion relations.The main content of this paper is divided into the following aspects:(2)The band gap of two dimensiona solid/solid lattice phononic crystals was studied.The energy band structure of two dimensiona tetragonal epoxy/tungsten phononic crystal is calculated by plane wave expansion method and finite element method.The influence of young’s modulus ratio and density ratio on energy band structure is analyzed,for example,the Dirac point and the degeneracy around the Dirac point.The three dimensional energy band diagram and the main deformation under different modes are given,and it is found that the stress concentration is easy to occur in the part where the matrix is combined with the scatterer,so the design of this part should be strengthened in the engineering application.(3)The band gap of two dimensiona steel/water type tetragonal phononic crystal was studied.The energy band structure and transfer loss of two dimensional steel/water phononic crystal are calculated by finite element method.The effects of different structure parameters and material parameters on band structure were studied.The energy band results of two dimensional steel/water phononic crystals are compared with other two dimensional solid/solid phononic crystals.(4)The energy band structure of traditional locally resonant phononic crystal is calculated.The influence of different structure parameters on the dispersion curve of the phononic crystal is analyzed and the structure is improved.A new local resonant phononic crystal structure is designed to widen the bandwidth of the low frequency band gap.The dispersion relation of locally resonant phononic crystal plate and its nonlinear vibration are studied.