Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity

doi:10.1088/1674-1056/20/12/124601

中国物理B ›› 2011, Vol. 20 ›› Issue (12): 124601-124601.doi: 10.1088/1674-1056/20/12/124601

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇下一篇

Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity

齐高娃, 侯国林, 阿拉坦仓

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

收稿日期:2011-08-16 修回日期:2011-08-16 出版日期:2011-12-15 发布日期:2011-12-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10962004) and the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 20080404MS0104).

Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity

Qi Gao-Wa(齐高娃), Hou Guo-Lin(侯国林)^†, and Alatancang(阿拉坦仓)

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Received:2011-08-16 Revised:2011-08-16 Online:2011-12-15 Published:2011-12-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10962004) and the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 20080404MS0104).

摘要/Abstract

摘要： The completeness theorem of the eigenfunction systems for the product of two 2×2 symmetric operator matrices is proved. The result is applied to 4×4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.

Abstract: The completeness theorem of the eigenfunction systems for the product of two 2×2 symmetric operator matrices is proved. The result is applied to 4×4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.

Key words: operator matrix, Hamiltonian operator, symplectic orthogonal, eigenfunction system, completeness

中图分类号: (Static elasticity)

46.25.-y

02.30.Jr (Partial differential equations) 02.30.Tb (Operator theory)

齐高娃, 侯国林, 阿拉坦仓. Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity[J]. 中国物理B, 2011, 20(12): 124601-124601.

Qi Gao-Wa(齐高娃), Hou Guo-Lin(侯国林), and Alatancang(阿拉坦仓) . Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity[J]. Chin. Phys. B, 2011, 20(12): 124601-124601.

参考文献 19

[1]	Zhong W X 1991 Chin. J. Comput. Mech. 8 229 (in Chinese)
[2]	Zhong W X 1994 Appl. Math. Mech. (English Edn.) 15 1113 %% 引用期刊的格式
[3]	Zhong W X 1995 A New Systematic Methodology for Theory of Elasticity (Dalian: Dalian University of Technology Press) (in Chinese)
[4]	Zhong W X and Yao W A 1999 Acta Mech. Sin. 31 173 (in Chinese)
[5]	Yao W A and Sun Z 2008 Chin. J. Theor. Appl. Mech. 40 557 (in Chinese)
[6]	Yao W A, Cai Z Y and Hu X F 2011 J. Dyn. Control 9 12 (in Chinese)
[7]	Lim C W, Li C F, Xiang Y and Yao W A 2009 Int. J. Engrg. Sci. 47 131
[8]	Xu X S, Zhong W X, Li X and Wang G P 2006 Int. J. Engrg. Sci. 44 897
[9]	Zhong Y, Li R, Liu Y M and Tian B 2009 Int. J. Solids Structures 46 2506
[10]	Chen W Q and Zhao L 2009 Chin. J. Theor. Appl. Mech. 41 588 (in Chinese)
[11]	Hou G L and Alatancang 2008 Chin. Phys. B 17 2753
[12]	Alatancang and Wu D Y 2008 Sci. Chin. Ser. A 38 904
[13]	Hou G L and Alatancang 2010 Commun. Theor. Phys. (Beijing) 53 237
[14]	Huang J J, Alatancang and Wang H 2009 Chin. Phys. B 18 3616
[15]	Huang J J, Alatancang and Wang H 2010 Chin. Phys. B 19 120101
[16]	Wang H, Alatancang and Huang J J 2011 Chin. Phys. B 20 010209
[17]	Luo J H, Li Q S and Liu G D 2009 Sci. Chin. Ser. G 52 270
[18]	Tang L M 1991 Chin. J. Comput. Mech. 8 343 (in Chinese)
[19]	Wu C X, Zhou Z Y and Ding P Z 1997 Chin. J. Comput. Phys. 14 702 (in Chinese)

Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity

Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 19

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Haiqin Wang(王海钦), and Xinpeng Xu(徐新鹏). Variational approximation methods for long-range force transmission in biopolymer gels[J]. 中国物理B, 2022, 31(10): 104602-104602.
[2]	Dongsheng Yang(杨东升), Guanting Liu(刘官厅). [J]. 中国物理B, 2020, 29(10): 104601-.
[3]	李勇, 马小娟, 刘其军, 孔歌星, 马海霞, 王文鹏, 汪贻高, 焦振, 刘福生, 刘正堂. Theoretics-directed effect of copper or aluminum content on the ductility characteristics of Al-based (Al₃Ti,AlTi,AlCu,AlTiCu₂) intermetallic compounds[J]. 中国物理B, 2016, 25(11): 113101-113101.
[4]	陈莘莘, 王娟, 李庆华. Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method[J]. 中国物理B, 2016, 25(4): 40203-040203.
[5]	吴德玉, 陈阿拉坦仓. On the ascent of infinite dimensional Hamiltonian operators[J]. 中国物理B, 2015, 24(8): 84601-084601.
[6]	秦洁宇, 杜刚, 刘晓彦. Investigation of strain effect on the hole mobility in GOI tri-gate pFETs including quantum confinement[J]. 中国物理B, 2014, 23(10): 108501-108501.
[7]	秦义校, 刘营营, 李中华, 杨明. An interpolating reproducing kernel particle method for two-dimensional scatter points[J]. , 2014, 23(7): 70207-070207.
[8]	宋宽, 侯国林, 阿拉坦仓. Block basis property of a class of 2×2 operator matrices and its application to elasticity[J]. 中国物理B, 2013, 22(9): 94601-094601.
[9]	李小林, 李淑玲. A meshless Galerkin method with moving least square approximations for infinite elastic solids[J]. 中国物理B, 2013, 22(8): 80204-080204.
[10]	郑鹤鹏, 蒋亦民, 彭政. Stress distribution and surface instability of an inclined granular layer[J]. Chin. Phys. B, 2013, 22(4): 40511-040511.
[11]	陈莘莘, 李庆华, 刘应华 . A scaled boundary node method applied to two-dimensional crack problems[J]. 中国物理B, 2012, 21(11): 110207-110207.
[12]	杨秀丽, 戴保东, 张伟伟. The complex variable meshless local Petrov–Galerkin method of solving two-dimensional potential problems[J]. 中国物理B, 2012, 21(10): 100208-100208.
[13]	白福浓, 李东明, 王健菲, 程玉民. [J]. 中国物理B, 2012, 21(2): 20204-020204.
[14]	丁宁, 方建会. Perturbation of symmetries for super-long elastic slender rods[J]. 中国物理B, 2011, 20(12): 120201-120201.
[15]	王华, 阿拉坦仓, 黄俊杰. On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications[J]. 中国物理B, 2011, 20(10): 100202-100202.