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A granular medium can be regarded as an equivalent uniform medium, of which the attenuation coefficient and the acoustic speed are obtained from the author's theory published elsewhere. The equivalent static density can be given by the mixed rule. According to the author's sound propagation theory in the granular medium, furthermore, the secondary waves are plane waves as well when the incidental sound wave is plane wave. In these cases, the three-dimensional equations can be simplified into a one-dimensional equation, and an expression for the viscosity coefficient in concentrated granular medium can be obtained. The theoretical results show that the viscosity coefficient depends on not only the volume fraction of the grains, but also sound frequency. On the other hand, the theory given in this paper can be used in the realistic cases, where less restrictions will be imposed on the applications than the Einstein's theory.
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Keywords:
- granular media /
- volume fraction /
- viscosity coefficients
[1] Knudsen V O, Wilson J V, Anderson N S 1948 Jour. Acoust. Soc. Am. 20 849
[2] Epstein P S, Richard R Carhart 1953 J. Acoust. Soc. Am. 25 553
[3] Wei R J 1954 Acta Phys. Sin. 10 187 [魏荣爵 1954 10 187]
[4] Wei R J, Wu J R 1981 Jour. Acoust. Soc. Am. 70 1213
[5] Landau L D, Lifshitz E M 1998 Fluid Mechanics (Beijing: World Pubishing Corporation) (2nd Ed) (流体力学 (第二版) (北京, 世界图书出版公司) pp73-75
[6] Qian Z W 1981 Acta Phys. Sin. 30 433 [钱祖文 1981 30 433]
[7] Qian Z W 1985 J. Sound Vib. 103 427
[8] Qian Z W 1986 J. Sound Vib. 108 147
[9] Qian Z W 1998 Acta Acustica 84 621
[10] Qian Z W 2008 Chinese J. Acousyics 33 385 [钱祖文 2008 声学学报 33 385]
[11] Qian Z W 2009 Chinese Journal of Acousyics 28 244
[12] Qian Z W 2009 Nonlinear Acoustics (2nd Ed.) (Beijing: Science Press) p76 [钱祖文 2009 非线性声学 (第二版 科学出版社)] 第76页
[13] Markham J J, Beyer R T, Lindsay R B 1951 Rev. Mod. Phys. 23 353
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[1] Knudsen V O, Wilson J V, Anderson N S 1948 Jour. Acoust. Soc. Am. 20 849
[2] Epstein P S, Richard R Carhart 1953 J. Acoust. Soc. Am. 25 553
[3] Wei R J 1954 Acta Phys. Sin. 10 187 [魏荣爵 1954 10 187]
[4] Wei R J, Wu J R 1981 Jour. Acoust. Soc. Am. 70 1213
[5] Landau L D, Lifshitz E M 1998 Fluid Mechanics (Beijing: World Pubishing Corporation) (2nd Ed) (流体力学 (第二版) (北京, 世界图书出版公司) pp73-75
[6] Qian Z W 1981 Acta Phys. Sin. 30 433 [钱祖文 1981 30 433]
[7] Qian Z W 1985 J. Sound Vib. 103 427
[8] Qian Z W 1986 J. Sound Vib. 108 147
[9] Qian Z W 1998 Acta Acustica 84 621
[10] Qian Z W 2008 Chinese J. Acousyics 33 385 [钱祖文 2008 声学学报 33 385]
[11] Qian Z W 2009 Chinese Journal of Acousyics 28 244
[12] Qian Z W 2009 Nonlinear Acoustics (2nd Ed.) (Beijing: Science Press) p76 [钱祖文 2009 非线性声学 (第二版 科学出版社)] 第76页
[13] Markham J J, Beyer R T, Lindsay R B 1951 Rev. Mod. Phys. 23 353
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