一类板弯曲方程的辛本征函数展开方法(英文)  

Symplectic Eigenfunction Expansion Approach for a Class of Rectangular Plates

作　　者：额布日力吐[1] 阿拉坦仓[1] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《应用数学》2013年第1期80-88,共9页Mathematica Applicata

基　　金：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);the SPHIMU(Z20100116,125120)

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.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.

关 键 词：矩形板 无穷维HAMILTON算子 本征函数系 完备性 一般解 

分 类 号：O175.3[理学—数学]