Abstract:Based on Biot and Bloch theory, the propagation characteristics of the anti-plane wave in a one-dimensional fluid-saturated porous phononic crystal are studied. The wave equation of the anti-plane wave in the fluid-saturated medium is solved. The transfer matrix between adjacent unit cells is obtained by using the interface continuity condition of stress and displacement; and the complex band structure of the unit cell is calculated by combining the transfer matrix with Bloch theory. The transmission spectrum of the phononic crystal is calculated using the stiffness matrix method. The influence of fluid viscosity, porosity and filling ratio on the anti-plane wave propagation is analyzed. The results show that as the viscosity coefficient increases, the imaginary part of the complex band structure first increases and then decreases, and the corresponding transmission is first weakened and then strengthened. The real part at the boundary of the first Brillouin-zone first becomes smooth and then sharp. These changes are consistent with that for fast longitudinal wave. With the increase of porosity, the density difference between the two kinds of porous media becomes larger. So, the band gap is widened and the attenuation is enhanced. Different from the fast compressional wave, the imaginary part for the high frequency passband remains zero with the change of porosity, because there is no interaction between the anti-plane wave and the slow longitudinal wave. As the decrease of filling ratio, it is found that the first band gap is widened and the corresponding attenuation is strengthened. The estimated midgap frequency values are consistent with the numerical results. However, the second band gap becomes first wider and then narrower, and the attenuation is first strengthened and then weakened.
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