Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates  

作　　者：WANG Hua Alatancang HUANG Jun-Jie 

机构地区：[1]School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China [2]Department of Mathematics, College of Science, Inner Mongolia University of Technology, Hohhot 010051, China

出　　处：《Communications in Theoretical Physics》2009年第12期1087-1092,共6页理论物理通讯（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant No.10962004;the Natural Science Foundation of Inner Mongolia under Grant No.2009BS0101;the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070126002;the Cultivation of Innovative Talent of "211 Project"of Inner Mongolia University

摘　　要：The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.

关 键 词：free vibration of rectangular thin plate double symplectic eigenfunction expansion method upper triangular matrix differential system general solution 

分 类 号：O551.3[理学—热学与物质分子运动论] O343.1[理学—物理]