对边简支的矩形平面弹性问题的辛本征展开定理

侯国林; 阿拉坦仓

doi:10.3879/j.issn.1000-0887.2010.10.005

对边简支的矩形平面弹性问题的辛本征展开定理

doi: 10.3879/j.issn.1000-0887.2010.10.005

内蒙古大学数学科学学院,呼和浩特 010021

基金项目: 国家自然科学基金资助项目(10962004);高等学校博士学科点专项科研基金资助项目(20070126002);内蒙古自治区自然科学基金资助项目(20080404MS0104)

详细信息

作者简介:
侯国林(1980- ),男,内蒙古人,教授,博士(E-mail:houguolin@163.com);阿拉坦仓(1963- ),男,内蒙古人,教授,博士,博士生导师(联系人.E-mail:alatanca@imu.edu.cn).

中图分类号: O175.3;O343.1
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出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-09-03
- 刊出日期: 2010-10-15

Symplectic Eigenfunction Expansion Theorem for the Rectangular Plane Elasticity Problems With Two Opposite Simply Supported

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China

摘要

摘要: 对来源于平面弹性问题的Hamilton算子的本征值问题进行了研究．在矩形域内含位移和应力的混合边界条件下,首先求解了相应算子的本征函数．接着,证明了本征函数系的完备性,这为施行分离变量法求解相应问题提供了可行性．最后,利用文中的辛本征展开定理获得了问题的一般解．
- 平面弹性问题 /
- Hamilton系统 /
- 辛正交性 /
- 本征展开 /
- Hamilton算子
Abstract: The eigenvalue problem of the Hamiltonian operator associated with the plane elasticity problems was investigated.First, the eigenfunctions of the operator with the mixed boundary conditions for the displacement and stress in the rectangular region was solved directly.Then, the completeness of the eigenfunctions was proved, thereby demonstrating the feasibility of using separation of variables to solve the problems.Finally, the general solution was obtained by using the symplectic eigenfunction expansion theorem.
- plane elasticity problems /
- Hamiltonian system /
- symplectic orthogonality /
- eigenfunction expansion /
- Hamiltonian operator

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参考文献(14)

[1]	阿拉坦仓, 张鸿庆, 钟万勰. 矩阵多元多项式的带余除法及其应用[J].应用数学和力学, 2000, 21(7): 661-668.
[2]	阿拉坦仓, 张鸿庆, 钟万勰. 一类偏微分方程的Hamilton正则表示[J].力学学报, 1999, 31(3): 347-357.
[3]	陈勇, 郑宇, 张鸿庆. 一些数学物理问题中的Hamilton方程[J].应用数学和力学, 2003, 24(1): 19-24.
[4]	REN Wen-xiu, Alatancang. An algorithm and its application for obtaining some kind of infinite-dimensional Hamiltonian canonical formulation[J]. Chinese Physics, 2007, 16 (11): 3154-3160. doi: 10.1088/1009-1963/16/11/002
[5]	Vainberg M M. Variational Methods for the Study of Nonlinear Operators[M]. San Francisco: Holden-Day, 1964.
[6]	钟万勰. 弹性力学求解新体系[M]. 大连: 大连理工大学出版社, 1995.
[7]	Lim C W, Lü C F, Xiang Y, Yao W. On new symplectic elasticity approach for exact free vibration solutions of rectangular Kirchhoff plates [J]. Int J Eng Sci, 2009, 47 (1):131-140. doi: 10.1016/j.ijengsci.2008.08.003
[8]	Yao W, Zhong W X, Lim C W. Symplectic Elasticity[M]. Singapore:World Scientific Publishing, 2009.
[9]	HOU Guo-lin, Alatancang. On the feasibility of variable separation method based on Hamiltonian system for plane magnetoelectroelastic solids[J]. Chinese Physics B, 2008, 17(8): 2753-2758. doi: 10.1088/1674-1056/17/8/001
[10]	HOU Guo-lin, Alatancang. Completeness of eigenfunction systems for off-diagonal infinite-dimensional Hamiltonian operators[J]. Commun Theor Phys, 2010,53(2): 237-241. doi: 10.1088/0253-6102/53/2/06
[11]	Alatancang, Wu D Y. Completeness in the sense of Cauchy principal value of the eigenfunction systems of infinite dimensional Hamiltonian operator[J]. Sci China Ser A, 2009,52(1): 173-180.
[12]	Zou G. An exact symplectic geometry solution for the static and dynamic analysis of Reissner plates[J]. Comput Methods Appl Mech Engrg, 1998, 156(1/4): 171-178. doi: 10.1016/S0045-7825(97)00204-1
[13]	Zhong Y, Li R. Exact bending analysis of fully clamped rectangular thin plates subjected to arbitrary loads by new symplectic approach[J]. Mechanics Research Communications, 2009,36(6): 707-714. doi: 10.1016/j.mechrescom.2009.04.001
[14]	Elias M S, Rami Shakarchi. Fourier Analysis: An Introduction[M].Oxford: Princeton University Press, 2003.

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对边简支的矩形平面弹性问题的辛本征展开定理

doi: 10.3879/j.issn.1000-0887.2010.10.005

作者简介:
侯国林(1980- ),男,内蒙古人,教授,博士(E-mail:houguolin@163.com);阿拉坦仓(1963- ),男,内蒙古人,教授,博士,博士生导师(联系人.E-mail:alatanca@imu.edu.cn).

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Symplectic Eigenfunction Expansion Theorem for the Rectangular Plane Elasticity Problems With Two Opposite Simply Supported

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对边简支的矩形平面弹性问题的辛本征展开定理

doi: 10.3879/j.issn.1000-0887.2010.10.005

作者简介: 侯国林(1980- ),男,内蒙古人,教授,博士(E-mail:houguolin@163.com);阿拉坦仓(1963- ),男,内蒙古人,教授,博士,博士生导师(联系人.E-mail:alatanca@imu.edu.cn).

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出版历程

Symplectic Eigenfunction Expansion Theorem for the Rectangular Plane Elasticity Problems With Two Opposite Simply Supported

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出版历程

目录

作者简介:
侯国林(1980- ),男,内蒙古人,教授,博士(E-mail:houguolin@163.com);阿拉坦仓(1963- ),男,内蒙古人,教授,博士,博士生导师(联系人.E-mail:alatanca@imu.edu.cn).