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

作　　者：王华 阿拉坦仓 黄俊杰 

机构地区：[1]School of Mathematical Sciences,Inner Mongolia University [2]College of Sciences,Inner Mongolia University of Technology

出　　处：《Chinese Physics B》2011年第1期92-97,共6页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.10962004and11061019);'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);the Cultivation of Innovative Talent of '211Project'of Inner Mongolia University

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.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 

分 类 号：O411.1[理学—理论物理] O151.21[理学—物理]