中国物理B ›› 2009, Vol. 18 ›› Issue (9): 3616-3623.doi: 10.1088/1674-1056/18/9/002
黄俊杰1, 阿拉坦仓1, 王华2
Huang Jun-Jie(黄俊杰)a), Alatancang(阿拉坦仓)a), and Wang Hua(王华)a)b)†
摘要: 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.
中图分类号: (Beams, plates, and shells)