The symplectic eigenfunction expansion theorem and its application to the plate bending equation
Huang Jun-Jie(黄俊杰)a), Alatancang(阿拉坦仓)a), and Wang Hua(王华)a)b)†
a School of Mathematical Sciences, Neimongol University, Hohhot 010021, China; b Department of Mathematics, College of Sciences, Neimongol University of Technology, Hohhot 010051, China
Abstract This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.
Received: 07 November 2008
Revised: 24 February 2009
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 10562002), the Natural
Science Foundation of Inner Mongolia, China (Grants No 200508010103
and 200711020106), and the Specialized Research Fund for the
Doctoral Program of Higher Education of China (Grant No
20070126002).
Cite this article:
Huang Jun-Jie(黄俊杰), Alatancang(阿拉坦仓), and Wang Hua(王华) The symplectic eigenfunction expansion theorem and its application to the plate bending equation 2009 Chin. Phys. B 18 3616
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.
