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Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground

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Abstract

The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground was studied. First, the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soils were transformed into a group of governing differential equations with 1-order by the technique of Fourier expanding with respect to azimuth, and the state equation is established by Hankel integral transform method, furthermore the transfer matrixes within layered media are derived based on the solutions of the state equation. Secondly, by the transfer matrixes, the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions, drainage conditions on the surface of ground as well as the contact conditions. Thirdly, the problem was led to a pair of dual integral equations describing the mixed boundaryvalue problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily. At the end of this paper, a numerical result concerning vertical and radical displacements both the surface of saturated ground and plate is evaluated.

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Authors and Affiliations

  1. Department of Civil Engineering and Architecture, Taizhou University, Taizhou, 318000, Zhejiang Province, P. R. China

    Wang Xiao-gang  (黄小岗)

Authors
  1. Wang Xiao-gang  (黄小岗)
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Correspondence to Wang Xiao-gang  (黄小岗).

Additional information

Communicated by HUANG Yi

Project supported by the National Natural Science Foundation of China (No. 50678108) and the Natural Science Foundation of Zhejiang Province (No. Y106264)

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Wang, Xg. Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground. Appl Math Mech 28, 1383–1396 (2007). https://doi.org/10.1007/s10483-007-1011-3

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  • DOI: https://doi.org/10.1007/s10483-007-1011-3

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2000 Mathematics Subject Classification

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