Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory

doi:10.1088/1674-1056/20/1/010209

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.

Keywords: operator matrix eigenvector completeness eigenvector expansion theorem

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

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Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory

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