弹性地基上矩形薄板的辛本征函数展开定理

Symplectic Eigenfunction Expansion Theorem of Rectangular Thin Plates on an Elastic Foundation

基于上三角Hamilton系统,研究了弹性地基上矩形薄板问题导出的Hamilton算子本征函数系的完备性,得到其本征展开的一种形式,并证明在另外一种形式下不完备.为此问题基于Hamilton系统的分离变量法提供了理论依据.

The bending problem of rectangular thin plates on an elastic foundation is written as an upper triangular infinite-dimensional Hamiltonian system.For the associated Hamiltonian operator,the completeness of the eigenfunction systems in one kind of form and the incompleteness in the other kind of form are proved,which offers theoretical guarantee for separation of variables based on the hamiltonian system for the bending problem.