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The dependences of the dynamic effective mass() and power dissipation p() of tungsten particles system on frequency are studied under vertical vibration excitation. It is found that there appears a sharp resonance peak in each of spectra of the real part M1 (), the imaginary part M2 () of the effective mass, and the power dissipation for a given vibrating strength. With the increase of the pressure acting on the top surface of the particle, each peak frequency of the M1 (), M2 () and power dissipation moves to higher frequency, and the peak height also increases accordingly. Further study finds that the resonance frequency fg of the real part of the effective mass satisfies piecewise power-law with the change of pressure P acting on the top surface. At low P value, the power exponent is 0.3, and at high P value the power exponent decreases to 1/6. The reciprocal of quality factor of the granular system, 1/Q, decreases exponentially with the change of pressure P.
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Keywords:
- granular matter /
- vertical vibration /
- effective mass /
- energy dissipation
[1] Brunet T, Jia X, Mills P 2008 Phys. Rev. Lett. 101 138001
[2] Zhang K S, Wang S, Zhu M, Ding Y, Hu Y 2013 Chin. Phys. B 22 014305
[3] Jaeger H M, Nagel S R, Behringer R P 1996 Rev. Mod. Phys. 68 1259
[4] Pak H, Behringer R 1993 Phys. Rev. Lett. 71 1832
[5] Windows-Yule C R K, Weinhart T, Parker D, Thornton A 2014 Phys. Rev. Lett. 112 098001
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[9] Wang W J, Kong X Z, Zhu Z G 2007 Phys. Rev. E 75 041302
[10] 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 62 024502]
[11] Hsu C J, Johnson D L, Ingale R A, Valenza J J, Gland N, Makse H A 2009 Phys. Rev. Lett. 102 058001
[12] Valenza J J, Hsu C J, Johnson D L 2010 J. Acoust. Soc. Am. 128 2768
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[14] Valenza J, Johnson D L 2012 Phys. Rev. E 85 041302
[15] Henann D L, Valenza J J, Johnson D L, Kamrin K 2013 Phys. Rev. E 88 042205
[16] Jiang Z H, Liu X Y, Peng Y J, Li J W 2005 Acta Phys. Sin. 54 5692 (in Chinese) [姜泽辉, 刘新影, 彭雅晶, 李建伟 2005 54 5692]
[17] Knight J B, Fandrich C G, Lau C N, Jaeger H M, Nagel S R 1995 Phys. Rev. E 51 3957
[18] Song C, Wang P, Makse H A 2008 Nature 453 629
[19] Nowak E R, Knight J B, Ben-Naim E, Jaeger H M, Nagel S R 1998 Phys. Rev. E 57 1971
[20] Kabla A, Debrégeas G 2004 Phys. Rev. Lett. 92 035501
[21] Kang W, Turner J A, Bobaru F, Yang L, Rattanidit K 2007 J. Acoust. Soc. Am. 121 888
[22] Digby P J 1981 J. Appl. Mech. 48 803
[23] Jia X, Caroli C, Velicky B 1999 Phys. Rev. Lett. 82 1863
[24] Cremer L, Heckl M, Ungar E 1973 Structure Borne Sound (Berlin: Springer) p141
[25] Goddard J D 1990 Proc. R. Soc. London A 430 105
[26] Pilbeam C C, Vaišnys J R 1973 J. Geophys. Res. 78 810
[27] Gardner G H F, Wyllie M R J, Droschak D M 1964 J. Petrol.Technol. 16 189
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[1] Brunet T, Jia X, Mills P 2008 Phys. Rev. Lett. 101 138001
[2] Zhang K S, Wang S, Zhu M, Ding Y, Hu Y 2013 Chin. Phys. B 22 014305
[3] Jaeger H M, Nagel S R, Behringer R P 1996 Rev. Mod. Phys. 68 1259
[4] Pak H, Behringer R 1993 Phys. Rev. Lett. 71 1832
[5] Windows-Yule C R K, Weinhart T, Parker D, Thornton A 2014 Phys. Rev. Lett. 112 098001
[6] Zhang J X, Xiong X M 2003 Acta Metall. Sin. 39 1127 (in Chinese) [张进修, 熊小敏 2003 金属学报 39 1127]
[7] Xiong X M, Wang H Y, Zhang J X 2003 Acta Metall. Sin. 39 1223 (in Chinese) [熊小敏, 王海燕, 张进修 2003 金属学报 39 1223]
[8] 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]
[9] Wang W J, Kong X Z, Zhu Z G 2007 Phys. Rev. E 75 041302
[10] 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 62 024502]
[11] Hsu C J, Johnson D L, Ingale R A, Valenza J J, Gland N, Makse H A 2009 Phys. Rev. Lett. 102 058001
[12] Valenza J J, Hsu C J, Johnson D L 2010 J. Acoust. Soc. Am. 128 2768
[13] Valenza J, Hsu C J, Ingale R, Gland N, Makse H A, Johnson D L 2009 Phys. Rev. E 80 051304
[14] Valenza J, Johnson D L 2012 Phys. Rev. E 85 041302
[15] Henann D L, Valenza J J, Johnson D L, Kamrin K 2013 Phys. Rev. E 88 042205
[16] Jiang Z H, Liu X Y, Peng Y J, Li J W 2005 Acta Phys. Sin. 54 5692 (in Chinese) [姜泽辉, 刘新影, 彭雅晶, 李建伟 2005 54 5692]
[17] Knight J B, Fandrich C G, Lau C N, Jaeger H M, Nagel S R 1995 Phys. Rev. E 51 3957
[18] Song C, Wang P, Makse H A 2008 Nature 453 629
[19] Nowak E R, Knight J B, Ben-Naim E, Jaeger H M, Nagel S R 1998 Phys. Rev. E 57 1971
[20] Kabla A, Debrégeas G 2004 Phys. Rev. Lett. 92 035501
[21] Kang W, Turner J A, Bobaru F, Yang L, Rattanidit K 2007 J. Acoust. Soc. Am. 121 888
[22] Digby P J 1981 J. Appl. Mech. 48 803
[23] Jia X, Caroli C, Velicky B 1999 Phys. Rev. Lett. 82 1863
[24] Cremer L, Heckl M, Ungar E 1973 Structure Borne Sound (Berlin: Springer) p141
[25] Goddard J D 1990 Proc. R. Soc. London A 430 105
[26] Pilbeam C C, Vaišnys J R 1973 J. Geophys. Res. 78 810
[27] Gardner G H F, Wyllie M R J, Droschak D M 1964 J. Petrol.Technol. 16 189
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