Applied Mathematics and Mechanics

, Volume 26, Issue 9, pp 1146–1157 | Cite as

Dynamic interaction between elastic thick circular plate and transversely isotropic saturated soil ground

Article
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Abstract

A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical harmonic source. However, the assumption may not always be valid. The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetrical harmonic force. The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established. By the technique of Fourier expansion and Hankel transform, the governing difference equations for transversely isotropic saturated soil are easily solved and the cooresponding Hankel trnasformed stress and displacement solutions are obtained. Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure. At the end, a numerical result is presented which indicates that on a certain frequency range, the displacement amplitude of the surface of the foundation increases with the increase of the frequency of the exciting force, and decreases in vibration form with the increase of the distance.

Key words

Biot's wave equation transversely isotropic saturated soil elastic circular plate non-axisymmetrical harmonic response Fredholm integral equation of the second kind 

Chinese Library Classification

O357.3 

2000 Mathematics Subject Classification

74L10 74K20 
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References

  1. [1]
    Chen Longzhu, Chen Shenli. Dynamic responses of elastic circular plate on saturated ground [J].Acta Mechanica Sinica, 2001,33(6): 821–827 (in Chinese).Google Scholar
  2. [2]
    Chen Shenli, Chen Longzhu. The vertical vibration of circular plate with rigid core footing on saturated ground[J].Acta Mechanica Sinica, 2002,34(1): 77–84 (in Chinese).Google Scholar
  3. [3]
    Jin Bo. Vertical vibration of a rigid circular plate with footing on a poroelastic half space with mixed boundary permeability condition[J].Acta Mechanica Solida Sinica, 1999,20(3): 267–271 (in Chinese).Google Scholar
  4. [4]
    Zhang Yinke, Huang Yi. The non-axisymmetrical dynamic response of transversely isotropic saturated poroelastic media[J].Applied Mathematics and Mechanics (English Edition), 2001,22(1): 63–78.CrossRefGoogle Scholar
  5. [5]
    Zhang Yinke, Huang Yi. Steady dynamic response of elastic saturated porous media under non-axisymmetrical load[J].China Civil Engineering Journal, 2002,35(3): 41–45 (in Chinese).Google Scholar
  6. [6]
    Kazi-Aoual, Guy Bonnet, Paul Jouanna. Green's founction in an infinite transversely isotropic saturated poroelastic medium[J].J Acoust Soc Am, 1988,84(5): 1883–1889.CrossRefGoogle Scholar
  7. [7]
    Huang Yi, Zhang Yuhong. Non-axisymmetrical Lamb's problems in saturated soils[J].Science in China (Ser E), 2000,30(4): 375–384 (in Chinese).Google Scholar
  8. [8]
    Cao Zhiyuan, Yang Shengtian.Dynamics of Thick Plate and Its Applications[M]. Science Press, Beijing, 1983, 36–38 (in Chinese).Google Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech 2005

Authors and Affiliations

  1. 1.School of Civil EngineeringXi'an University of Architecture & TechnologyXi'anP. R. China
  2. 2.Department of Civil EngineeringQinghai UniversityXiningP. R. China

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