|
|
Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory |
Wang Hua(王华)a)b),Alatancang(阿拉坦仓)a), and Huang Jun-Jie(黄俊杰)a)† |
a School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; b College of Sciences,Inner Mongolia University of Technology, Hohhot 010051, China |
|
|
Abstract This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates.
|
Received: 28 June 2010
Revised: 02 August 2010
Accepted manuscript online:
|
PACS:
|
02.30.Tb
|
(Operator theory)
|
|
02.30.Jr
|
(Partial differential equations)
|
|
46.25.-y
|
(Static elasticity)
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10962004 and 11061019), 'Chunhui Program' Ministry of Education(Grant No. Z2009-1-01010), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070126002), the Doctoral Foundation of Inner Mongolia (Grant No. 2009BS0101), the Natural Science Foundation of Inner Mongolia (Grant No. 2010MS0110) and the Cultivation of Innovative Talent of '211 Project' of Inner Mongolia University. |
Cite this article:
Wang Hua(王华), Alatancang(阿拉坦仓), and Huang Jun-Jie(黄俊杰) Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory 2011 Chin. Phys. B 20 010209
|
[1] |
Zhong W X 1991 Computational Structural Mechanics and Applications 8 229
|
[2] |
Zhong W X 1995 A New Systematic Methodology for Theory of Elasticity (Dalian: Dalian University of Technology Press)
|
[3] |
Zhou Z H, Xu X S and Leung A V T 2009 International Journal of Solids and Structures 46 3577
|
[4] |
Yao W A and Sui Y F 2004 Applied Mathematics and Mechanics 25 178
|
[5] |
Yao Z, Zhang H W, Wang J B and Zhong W X 2008 Chinese Journal of Solid Mechanics bf29 13
|
[6] |
Huang J J, Alatancang and Wang H 2009 Chin. Phys. B 18 3616
|
[7] |
Alatancang, Huang J J and Fan X Y 2008 Science in China Series A-Mathematics 51 915
|
[8] |
Huang J J, Alatancang and Chen A 2008 Acta Mathematicae Applicatae Sinica Chinese Series 31 457
|
[9] |
Wang H, Alatancang and Huang J J 2009 Commun. Theor. Phys. 52 1087
|
[10] |
Alatancang and Wu D Y 2009 Science in China Series A-Mathematics 52 173
|
[11] |
Huang J J, Alatancang and Wang H 2010 Chin. Phys. B 19 120201
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|