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The symplectic eigenfunction expansion theorem and its application to the plate bending equation |
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| Authors: | Huang Jun-Jie Alatancang and Wang Hua |
| Affiliation: | School of Mathematical Sciences, Neimongol University, Hohhot 010021, China; School of Mathematical Sciences, Neimongol University, Hohhot 010021, China;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. |
| Keywords: | plate bending equation symplectic eigenfunction expansion theorem infinite dimensional Hamiltonian operator analytical solution |
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