关键词: 颗粒物质/
声速/
非线性/
声衰减
English Abstract
Numerical study on acoustic behavior of two-dimensional granular system
Liu Xiao-Yu1,Zhang Guo-Hua1,
Sun Qi-Cheng2,
Zhao Xue-Dan1,
Liu Shang1
1.Department of Physics, University of Science and Technology Beijing, Beijing 100083, China;
2.State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 11272048, 11572178, 91634202).Received Date:15 May 2017
Accepted Date:17 July 2017
Published Online:05 December 2017
Abstract:The transversal and longitudinal wave velocities, the acoustic attenuation coefficients, the nonlinear coefficients at different pressures and the acoustic attenuation coefficient as a function of frequency in a two-dimensional (2D) monodisperse disc system are numerically calculated. The results show that the transversal and longitudinal wave velocities both exhibit a piecewise power law with pressure P. When P -4, the velocity decreases with the increase of pressure in the 2D disc granular system, and when P > 10-4, the transversal wave velocity Vt and longitudinal wave velocity Vl show the scaling power laws, i.e., νt~P0.202 and vl~P0.338, respectively. The ratio of the shear modulus to the bulk modulus G/B shows a power law scaling with the pressure, G/B~P-0.502, implying that the system lies in an L glass state at low pressure, similar to that of a three-dimensional (3D) spherical granular system. The attenuation coefficients (αT, αL) of the horizontal excitation and vertical excitation also show the picecewise behaviors with the change of frequency f. When f f. When f > 0.05, α ∝ fTα, αL ∝ f. And when f > 0.35, αT ∝ f2 and αL ∝ f1.5. In addition, the nonlinear coefficient and the attenuation coefficient of the 2D disc granular system under the vertical and horizontal excitation both also show a piecewise law behavior with pressure, similar to that of the acoustic velocity. When P -4, only the transversal nonlinear coefficient changes according to βT ∝ P-0.230, while the other coefficient has no change. When P > 10-4, the attenuation coefficients and nonlinear coefficients decrease according to their power law with the increase of pressure, i.e., βT ∝ P-0.703, βL ∝ P-0.684, αT ∝ P-0.099, αL ∝ P-0.105. The characteristic length l*, which characterizes the disordered structure responsible for the scattering, also decreases according to power law with the increase of pressure, when P -4, l* ∝ P-0.595; when P > 10-4, l* ∝ P0.236.
Keywords: granular matter/
acoustic velocity/
nonlinear/
acoustic attenuation
