| Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground |
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| 作者姓名： | 黄小岗 |
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| 作者单位： | Department of |
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| 基金项目： | 国家自然科学基金;浙江省自然科学基金 |
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| 摘 要： | 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 ex- panding 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 boundary- value 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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| 关 键 词： | 横向各向同性 分层饱和地基 积分方程 弹性圆盘 非轴对称振动 |
| 收稿时间： | 16 January 2006 |
| 修稿时间： | 2006-01-16 |
Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground |
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| Wang?Xiao-gang.Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground[J].Applied Mathematics and Mechanics(English Edition),2007,28(10):1383-1396. |
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| Authors: | Wang Xiao-gang |
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| Institution: | Department of Civil Engineering and Architecture, Taizhou University,Taizhou 318000, Zhejiang Province, P. R. China |
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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 ex- panding 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 boundary- value 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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| Keywords: | transversely isotropic layered saturated ground Biot's motion equations elastic circular plate Fredholm integral equation |
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