Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78713-8029, USA.
J Acoust Soc Am. 2011 Jun;129(6):3531-43. doi: 10.1121/1.3571421.
It is shown that the shear wave speed in a granular medium is less than that in an elastic solid of the same shear modulus-to-density ratio. Shear and compressional wave speeds are derived for granular media using a conservation of energy approach. The grains are assumed to be spherical with elastic Hertzian contacts of constant stiffness. The affine approximation is used to determine the relative displacements of grain centers, and it is also assumed that the grains are small compared to a wavelength, consistent with the effective medium approximation. Potential and kinetic energies associated with linear motion are the same as those in an elastic solid, but it is found that shear wave propagation in a granular medium involves additional energies associated with grain rotation. The partition of energies results in a reduction in the shear wave speed, relative to an elastic solid of the same shear modulus-to-density ratio. It is shown that the reduction is an inherent property of granular media, independent of any departure from the affine approximation or fluctuations in coordination number or contact stiffness. The predicted wave speed ratios are consistent with published measurements.
研究表明，颗粒介质中的剪切波速度小于具有相同剪切模量-密度比的弹性固体中的剪切波速度。使用能量守恒方法推导出了颗粒介质中的剪切波和压缩波速度。假设颗粒为球形，具有恒定刚度的弹性赫兹接触。采用仿射近似法确定颗粒中心的相对位移，同时假设颗粒的尺寸与波长相比很小，符合有效介质近似法。与弹性固体中相同的线性运动的势能和动能，但发现颗粒介质中的剪切波传播涉及与颗粒旋转相关的附加能量。能量分配导致剪切波速度相对于具有相同剪切模量-密度比的弹性固体降低。结果表明，这种降低是颗粒介质的固有特性，与仿射近似的任何偏离或配位数或接触刚度的波动无关。预测的波速比与已发表的测量结果一致。
