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中文摘要：
本文研究一边简支对边滑支边界条件的矩形板方程的无穷维Hamilton算子本征函数系，证明该无穷维Hamilton算子广义本征函数系在Cauchy主值意义下是完备的，为应用辛本征函数展开法求解该平面弹性问题提供理论基础．进而推导出原方程的通解，并对该平面弹性问题指出什么样的边界条件可按此方法求解．最后应用具体的算例说明所得结论的合理性．
英文摘要：
The eigenfunction system of the infinite dimensional Hamiltoniart operator appearmg m 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 sys- tem is proved. It offers a theoretical basis to solve the plane elasticity problem by the symplectic el- genfunction expansion method. Then the general rived. Furthermore it is indicated what boundary solved by this method. Finally, the validity of the solutions for the plane elasticity problem is de- conditions for the plane elasticity problem can be obtained results is verified by a specific example.
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