中国物理B ›› 2011, Vol. 20 ›› Issue (1): 10209-010209.doi: 10.1088/1674-1056/20/1/010209

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

阿拉坦仓1, 黄俊杰1, 王华2   

  1. (1)School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; (2)School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China;College of Sciences,Inner Mongolia University of Technology, Hohhot 010051, China
  • 收稿日期:2010-06-28 修回日期:2010-08-02 出版日期:2011-01-15 发布日期:2011-01-15
  • 基金资助:
    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.

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)†   

  1. a School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; b College of Sciences,Inner Mongolia University of Technology, Hohhot 010051, China
  • Received:2010-06-28 Revised:2010-08-02 Online:2011-01-15 Published:2011-01-15
  • Supported by:
    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.

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摘要： 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.

关键词: operator matrix, eigenvector, completeness, eigenvector expansion theorem

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.

Key words: operator matrix, eigenvector, completeness, eigenvector expansion theorem

中图分类号:  (Operator theory)

  • 02.30.Tb
02.30.Jr (Partial differential equations) 46.25.-y (Static elasticity)