Green Quasifunction Method for Vibration of Simply-Supported Thin Polygonic Plates on Pasternak Foundation

YUAN Hong; LI Shan-qing; LIU Ren-huai

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(7): 757-762

YUAN Hong, LI Shan-qing, LIU Ren-huai. Green Quasifunction Method for Vibration of Simply-Supported Thin Polygonic Plates on Pasternak Foundation[J]. Applied Mathematics and Mechanics, 2007, 28(7): 757-762.

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Green Quasifunction Method for Vibration of Simply-Supported Thin Polygonic Plates on Pasternak Foundation

Institute of Applied Mechanics, Jinan University, Guangzhou 510632, P. R. China

Received Date: 2006-10-17
Rev Recd Date: 2007-04-23
Publish Date: 2007-07-15

Abstract

Abstract

A new numerical method-Green quasifunction method is proposed. The idea of Green quasifunction method was clarified in detail by considering vibration problem of simply-supported thin polygonic plates on Pasternak foundation. A Green quasifunction was established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The mode shape differential equation of vibration problem of simply-supported thin plates on Pasternak foundation was reduced to two simultaneous Fredholm integral equations of the second kind by Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations was overcome. Finally, natural frequency was obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the Green quasifunction method.
- Green function,
- integral equation,
- vibration of thin plate,
- Pasternak foundation

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References(9)

References

[1]	Winkler E.Die Lehre von der Elastigitat und Festigkeit[M].Dominicus:Prague,1867.
[2]	Salvadurai A D S.Elastic Analysis of Soil Foundation Interaction[M].London:Elsevier Scientific Publishing Co,1979.[WT5”BZ]. Рвачев Β Л.Теория　R-Функции и Некторые　ее　Приложения[M].Киев:Наук　Думка,1982,415-421.
[4]	袁鸿.Winkler地基上薄板问题的准格林函数方法[J].计算力学学报,1999,16(4):478-482.
[5]	陆伟,袁鸿.准格林函数方法在Winkler地基上简支平行四边形板中的应用[J].暨南大学学报(自然科学与医学版),2006,27(1):81-86.
[6]	王红,袁鸿.准格林函数方法在弹性扭转问题中的应用[J].华南理工大学学报(自然科学版),2004,32(11):86-88.
[7]	王红,袁鸿.R-函数理论在梯形截面柱弹性扭转问题中的应用.华中科技大学学报(自然科学版),2005,33(11):99-101.
[8]	郑建军,樊承谋.双参数地基板振动的中值定理[J].上海力学,1995,16(2):166-171.
[9]	Ortner V N.Regularisierte faltung von distributionen． Teil 2: Eine tabelle von fundamentallocunngen[J].Zeitschrift Fur Angewandte Mathematik und Physik,1980,31(1):155-173. doi: 10.1007/BF01601710
[10]	Kurpa L V. Solution of the problem of deflection and vibration of plates by the R-function method[J].Sov Appl Mech,1984,20(5):470-473. doi: 10.1007/BF00885200