摘要:
数值测量了卸载过程中二维单分散圆盘颗粒系统的横波、纵波声速、声衰减系数、非线性系数随压强的变化以及声衰减系数随频率的变化.结果表明,二维(2D)圆盘颗粒体系的横波、纵波声速均随压强呈分段幂律标度:当压强P<10-4时,横波、纵波声速随压强的增大而减小;当P>10-4时,有vt～P 0.202,vl～P 0.338.进一步得到其剪切模量和体积模量的比值G/B也随压强呈幂律标度,G/B～P-0.502,暗示在低压强下,与三维(3D)球形颗粒体系类似,2D圆盘颗粒体系也处于L玻璃态.水平激励和垂直激励下2D圆盘颗粒系统的衰减系数随频率变化也呈现分段行为:当频率f<0.05时,衰减系数不随f变化;当f>0.05时,横波纵波的衰减系数 α ～f;当f>0.35时,横波衰减系数 αT～f 2,纵波衰减系数 αL～f 1.5.此外,竖直水平激励下的2D圆盘颗粒系统的非线性系数和衰减系数随压强也呈现与声速类似的分段规律:当P<10-4时,横波非线性系数 βT～P-0.230,其余都不随压强变化.当P>10-4时,两者均随压强增大呈幂律减小:βT～P-0.703,βL～P-0.684,αT～P-0.099,αL～P-0.105.进而得到2D圆盘颗粒系统中散射相关的特征长度 ?? 随压强呈幂律标度,当P<10-4时,?? ～P-0.595;当P>10-4时,?? ～P 0.236.
关键词:
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颗粒物质
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声速
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非线性
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声衰减
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 < 10-4, 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., vt ～ P 0.202 and vl ～ P 0.338, 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 < 0.05, neither of the two attenuation coefficients changes with frequency f. When f > 0.05, α ∝ f αT , αL ∝ f. And when f > 0.35, αT ∝ f 2 and αL ∝ f 1.5. 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 < 10-4, 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 ??, which characterizes the disordered structure responsible for the scattering, also decreases according to power law with the increase of pressure, whenP < 10-4, ?? ∝ P -0.595; when P > 10-4, ?? ∝ P 0.236.
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