应用数学2013，Vol.26Issue(1)：80-88,9.
一类板弯曲方程的辛本征函数展开方法
Symplectic Eigenfunction Expansion Approach for a Class of Rectangular Plates
摘要
Abstract
The eigenfunction system of the infinite dimensional Hamiltonian operator appearing in the rectangular plates with one side simply supported and the opposite side slidingly supported is studied.In the sense of Cauchy's principal value,the completeness of the extended eigenfunction system is proved.It offers a theoretical basis to solve the plane elasticity problem by the symplectic eigenfunction expansion method.Then the general solutions for the plane elasticity problem is derived.Furthermore;it is indicated what boundary conditions for the plane elasticity problem can be solved by this method.Finally,the validity of the obtained results is verified by a specific example.关键词
矩形板/无穷维Hamilton算子/本征函数系/完备性/一般解Key words
Rectangular plate / Infinite dimensional Hamiltonian operator/Eigenfunction system/ Completeness / General solution分类
数理科学引用本文复制引用
额布日力吐,阿拉坦仓..一类板弯曲方程的辛本征函数展开方法[J].应用数学,2013,26(1):80-88,9.基金项目
Supported by the National Natural Science Foundation of China(10962004,11061019),the Specialized Research Fund for the Doctoral Program of Higher Education of China (20111501110001),and the SPHIMU(Z20100116,125120) （10962004,11061019）
