Research On The Elastic Wave Propagation In Periodic Structures

Nowadays, the research on the characteristics of elastic wave propagation in the material of periodic structures is very popular, mainly because of the band gap being produced during the elastic wave propagation in the material of periodic structures, which can be used in the design of new functional materials. The propagation of elastic wave in a periodic structure is influenced by the geometrical parameters of the internal structure and the material parameters. In this paper, we study the influence of the shape and the shear modulus of the scattering body on the acoustic band gap, and the relationship between the volume fraction and the fundamental frequency of the elastic wave in the periodic structure. The main research work includes:In two-dimensional infinite periodic structure, representative element is selected and periodic boundary conditions are imposed by the Bloch theorem. What's more, two sets of grid can work out complex calculations, which is a defect of ABAQUS. The two sets of grid are exactly the same, one is to be applied to solve the real part of the equation, wile another is to be applied to solve the imaginary part of the equation, so that I can obtain the frequency dispersion relation curve.This paper studies the effect of pore shape and the shear modulus of the diffuser on the acoustic band gap. The scattering body is arranged in a square shape, then the shape is gradually changed from a circle to an ellipse, leading to that the ratio of the short axis to the long axis of the ellipse is close to zero. The study shows that the scattering body has a band gap when it is a circular hole. The band gap disappears when the ratio of the short axis to the long axis gets gradually smaller. The effect of shear modulus on the acoustic band gap is studied by using the elastic material with different shear modulus in the circular hole. The simulation analysis shows that the larger order of the magnitude between the matrix and the shear modulus of the scattering body is, the larger the band gap is.The segment of the pore structure in periodic structure is usually random. In this paper, the volume fraction of pores in the control cell holes simulates random pores distribution, from which I can get the results of calculation of 50 different random structures. The statistical analysis shows that with the increase of the void volume fraction, the fundamental frequency of limitless major cycle structure gradually decreases, and also, it has a linear relationship with the pore volume percentage.The innovation of this paper lies in using two sets of grid to research elastic wave propagation in periodic structures, adopting numerical simulation method to establish the relationship between the fundamental frequency of the elastic wave propagation in random structure and the scattering volume fraction.