Torsional Vibrations of a Rigid Circular Plate on Transversely Isotropic Saturated Soil

WU Da-zhi; CAI Yuan-qiang; XU Chang-jie; ZHAN Hong

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Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(11): 1349-1356

WU Da-zhi, CAI Yuan-qiang, XU Chang-jie, ZHAN Hong. Torsional Vibrations of a Rigid Circular Plate on Transversely Isotropic Saturated Soil[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1349-1356.

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Torsional Vibrations of a Rigid Circular Plate on Transversely Isotropic Saturated Soil

1.
Department of Civil Engineering, Zhejiang University, Hangzhou 310027, P. R. China;

Received Date: 2004-11-16
Rev Recd Date: 2006-06-20
Publish Date: 2006-11-15

Abstract

Abstract

An analytical method is presented for the torsional vibrations of a rigid disk resting on transversely isotropic saturated soil.By employing the technique of Hankel transform,the dynamic governing differential equations for transversely isotropic saturated poroelastic medium were solved. Considering the mixed boundary-value conditions,the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established.By appropriate transform,the dual integral equations were converted into a Fredholm integral equation of the second kind.Subsequently,the dynamic compliance coefficient,the torsional angular amplitude of the foundation and the contact shear stress were expressed explicitly.Selected examples are presented to analyse the influence of saturated soil.s anisotropy on the foundation.s vibrations.
- transversely isotropic saturated soil,
- torsional vibration,
- rigid circular plate,
- dynamical compliance coefficient,
- contact shear stress

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References(11)

References

[1]	Biot M A. Theory of propagation of elastic waves in a fluid-saturated porous solid[J].J Acoust Soc Amer,1956,28(2):168—191. doi: 10.1121/1.1908239
[2]	Biot M A. Mechanics of deformation and acoustic propagation in porous media[J].J Appl Phys,1962,33(4):1482—1498. doi: 10.1063/1.1728759
[3]	JIN Bo,LIU Hua. Vertical dynamic response of a disk on a saturated poroelastic half-space[J].Soil Dynamic and Earthquake Engineering,1999,18(6):437—443. doi: 10.1016/S0267-7261(99)00013-5
[4]	Philippacopoulos A J.Axisymmetric vibration of disk resting on saturated layered half-space[J].Journal of Engineering Mechanics,1989,115(10):2301—2322. doi: 10.1061/(ASCE)0733-9399(1989)115:10(2301)
[5]	CHEN Long-zhu,WANG Guo-cai.Torsional vibrations of elastic foundation on saturated media[J].Soil Dynamic and Earthquake Engineering,2002,22(3):223—227. doi: 10.1016/S0267-7261(02)00012-X
[6]	Payton R G.Elastic Wave Propagation in Transversely Isotropic Media[M].Hague: Martinus Nijhoff Publishers,1983,130—185.
[7]	Tsai Y M.Torsional vibrations of a circular disk on an infinite transversely isotropic medium[J].Internat J Solids and Structures,1989,25(9):1069—1076. doi: 10.1016/0020-7683(89)90022-X
[8]	Kazi-Aoual M N, Bonnet G, Jouanna P. Green's functions in an infinite transversely isotropic saturated poroelastic medium[J].J Acoust Soc Amer,1988,84(5):1883—1889. doi: 10.1121/1.397153
[9]	Abouseiman Y, Cui L. Poroelastic solutions in transversely isotropic media for wellbore and cylinder[J].Inter J Solids and Structures,1998,35(35):4905—4929. doi: 10.1016/S0020-7683(98)00101-2
[10]	丁皓江.横观各向同性弹性力学[M].杭州:浙江大学出版让,1997，5—18.
[11]	Nobel B. The solution of Bessel function dual integral equation by a multiplying factor method[J].Proceeding Comb Philosophical Society,1963,59(2):351—362. doi: 10.1017/S0305004100036987