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对颗粒物质的有效质量谱及耗散功率进行了数值研究，发现水平和垂直激励下颗粒体系的共振频率fg与体积模量k均随压强P呈分段幂律变化，在高压强下遵循fg∝P1/6，k∝P1/3的规律，在低压强下遵循fg∝P1/4，k∝P1/2的规律.同时，在水平和垂直振动下，颗粒体系品质因子的倒数1/Q随P的变化呈指数衰减.在特定频率和压强下，颗粒体系的平均耗散功率p随振动强度Γ的变化曲线上存在一个特征振动强度Γ*，当ΓΓ*时，颗粒体系表现出类固态行为，平均耗散功率p随振动强度Γ呈幂律标度，p∝Γα（2αΓ >Γ*时，颗粒体系表现出类液态行为，体系的平均耗散功率p随振动强度Γ呈线性变化.由此得到了水平激励下颗粒体系类固体类流体转变的Γ-P相图.In this paper, in order to explore the movement characteristics of granular system under the horizontal and vertical excitation, the effective mass spectrum and dissipation power of granular material are studied by numerical simulation. We use LIGGGHTS software to simulate a granular system consisting of 13340 dispersed particles in a cubic container. For the two different vibration directions of granular system (horizontal and vertical), we carry out a pressure unloading experiment in a pressure range from 1012.10 kPa to 8.66 kPa. It is found that under the horizontal and vertical excitation, the resonance frequency fg and volume modulus k of granular system satisfy piecewise power-law with the change of pressure P applied to the top surface. It follows the laws, that is, fg∝P1/6 and k∝P1/3 at low pressure and fg∝P1/4 and k∝P1/2 at high pressure. At the same time, according to the effective mass of the imaginary part, we can obtain the dissipative characteristics of the granular system. Under the horizontal and vertical excitation, the reciprocal of quality factor of granular matter, 1/Q, decreases exponentially with the change of pressure P. In the relaxation dynamics of the granular system, both the acceleration and the stress play a role similar to the role of temperature in the thermal system. In order to further study the influence of acceleration on solid-fluid-like transition of granular system, we measure the relationships between the dissipation power and the vibration intensity (1g-30g) under different pressures (8.66-1012.10 kPa), in the horizontal vibration (500 Hz). At the fixed frequency and pressure, there is a characteristic vibration intensity Γ* in the curve of the average power dissipation of granular system with vibration intensity Γ. When ΓΓ*, the granular system exhibits a solid-like behavior, and the variation of the average power dissipation with the change of vibration intensity Γ shows a power-law scaling, p∝Γα (2αΓ > Γ*, the granular system exhibits a liquid-like behavior, and the variation of the average power dissipation of granular system with the vibration intensity Γ changes into a linear fashion. Then, the phase diagram of transition from the solid-like phase to fluid-like phase, i.e., Γ-P phase diagram, in granular system under the horizontal excitation, is obtained in this paper.
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Keywords:
- granular matter /
- horizontal vibration /
- effective mass /
- solid-like to fluid-like transition
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[21] 2015 Acta Phys. Sin. 64 044501 (in Chinese)[余田, 张国华, 孙其诚, 赵雪丹, 马文波2015物理学报64 044501]
[22] Xu N 2011 Front. Phys. 6 109
[23] Lastakowski H, Géminard J C, Vidal V 2015 Sci. Rep.-UK 5 13455
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[1] Lu K Q, Liu J X 2004 Physics 33 629 (in Chinese)[陆坤权, 刘寄星2004物理33 629]
[2] Sun Q, Jin F, Zhou G D 2013 Granular Mat. 15 119
[3] Bi Z, Sun Q, Jin F, Zhang M 2011 Granular Mat. 13 503
[4] Peyneau P E, Roux J N 2008 Phys. Rev. E 78 041307
[5] Majmudar T S, Behringer R P 2005 Nature 435 1079
[6] Sun Q C, Wang G Q 2008 Acta Phys. Sin. 57 4667 (in Chinese)[孙其诚, 王光谦2008物理学报57 4667]
[7] Zhou G D, Sun Q C 2013 Powder Technol. 239 115
[8] Sun Q C, Wang G Q, Hu K H 2009 Prog. Nat. Sci. 19 523
[9] Karimi K, Maloney C E 2011 Phys. Rev. Lett. 107 268001
[10] Wortel G H, van Hecke M 2015 Phys. Rev. E 92 040201
[11] Wang P P, Wang W J, Liu C S, Zhu Z G 2009 Rock Soil Mech. 30 (Supp.) 129(in Chinese)[汪盼盼, 王万景, 刘长松, 朱震刚2009岩土力学30 (增刊) 129]
[12] Valenza J, Hsu C J, Ingale R, Gland N, Makse H A, Johnson D L 2009 Phys. Rev. E 80 051304
[13] Hsu C J, Johnson D L, Ingale R A, Valenza J J, Gland N, Makse H A 2009 Phys. Rev. Lett. 102 058001
[14] Valenza J, Johnson D L 2012 Phys. Rev. E 85 041302
[15] Peng Z, Jiang Y M, Liu R, Hou M Y 2013 Acta Phys. Sin. 62 024502 (in Chinese)[彭政, 蒋亦民, 刘锐, 厚美瑛2013物理学报62 024502]
[16] Ansari I H, Alam M 2016 Phys. Rev. E 93 052901
[17] Eshuis P, van der Weele K, van deer Meer D, Lohse D 2005 Phys. Rev. Lett. 95 258001
[18] Eshuis P, van der Weele K, van der Meer D, Bos R, Lohse D 2007 Phys. Fluids 19 123301
[19] Garcimartín A, Pastor J M, Arévalo R, Maza D 2007 Eur. Phys. J. Spec. Top. 146 331
[20] Saluña C, Pöschel T 2000 Eur. Phys. J. E 1 55
[21] 2015 Acta Phys. Sin. 64 044501 (in Chinese)[余田, 张国华, 孙其诚, 赵雪丹, 马文波2015物理学报64 044501]
[22] Xu N 2011 Front. Phys. 6 109
[23] Lastakowski H, Géminard J C, Vidal V 2015 Sci. Rep.-UK 5 13455
[24] Goddard J D 1990 Proc. R. Soc. Lond. A 430 105
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