梯度饱和多孔材料中弹性波的截止频率

Analysis of cut-off frequencies for functionally graded fluid-saturated materials

基于Biot多孔介质理论,应用WKB(Wentzel-Kramers-Brillouin)法,推导得到SH波和Lamb波在梯度非均匀含液饱和材料中截止频率的解析表达式.求解过程中应用波数趋于零的极限条件,通过简化控制方程,获得平面SH波和P-SV波的截止频率.问题的解答揭示了截止频率与材料的物理力学性质以及非均匀性密切相关.考虑材料参数沿板厚按指数形式变化的饱和多孔板,通过数值算例分析弹性平面波在该类非均质饱和多孔材料中的截止频率变化规律.数值结果表明,截止频率随着板的厚度、孔隙率和非均匀参数及渗透系数的不同均有显著的变化,验证了计算结果满足精确性要求.

The analytical expression for the cut-off frequencies of the horizontal shear waves（SH wave）and Lamb waves（P-SV wave）in a functionally graded inhomogeneous fluid-saturated media was deduced by applying the WKB（Wentzel-Kramers-Brillouin）method based on Biot＇s theory of poroelastic medium.In the process of solving,the cut-off frequencies of SH wave and P-SV wave were obtained with the limiting condition of the wave number approaching zero by simplifying the governing equation.The solution to the problem revealed that the cut-off frequencies were closely associated with the physicomechanical properties and the heterogeneity of the material.The material parameter of the fluid-saturated poroelastic plate changing along the thickness direction as an exponential form was considered.The changing regularity of the elastic plane wave＇s cut-off frequencies in the inhomogeneous fluid-saturated porous plate was analyzed by numerical examples.The numerical results showed that the cut-off frequencies were related to the material properties of the fluid-saturated material,including thickness of the plate,porosity,gradient index and permeability.The accuracy of the numerical solution was validated.