四边固支正交各向异性矩形薄板弯曲问题的辛叠加方法  

Analytical Bending Solutions of Clamped Orthotropic Rectangular Thin Plates With the Symplectic Superposition Method

作　　者：额布日力吐[1] 冯璐[1] 阿拉坦仓[1,2] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]呼和浩特民族学院,呼和浩特010051

出　　处：《应用数学和力学》2018年第3期311-323,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11362011;11371185;11761029);内蒙古自然科学基金(2013MS0103)~~

摘　　要：将正交各向异性矩形薄板方程化为Hamilton系统,利用分离变量法给出相应的无穷维Hamilton算子,进而计算出该无穷维Hamilton算子的本征值及对应的本征函数系,并分别证明了本征函数系的辛正交性及完备性.之后利用辛叠加方法,求出正交各向异性矩形薄板弯曲问题的解析解.最后通过算例验证了所得解析解的正确性.The orthotropic rectangular thin plate equations were transformed into the Hamiltonian system,and the corresponding infinite dimensional Hamiltonian operator was obtained with the method of separation of variables. Then the eigenvalues and corresponding eigenfunctions of the Hamiltonian operator were calculated,and the eigenfunction system was proved to be of symplectic orthogonality and completeness.Finally,with the symplectic superposition method,the analytical bending solutions of fully clamped orthotropic rectangular thin plates were presented. The comparison between the analytical solutions and the numerical examples shows the correctness of the proposed method.

关 键 词：正交各向异性薄板 无穷维HAMILTON算子 本征函数系 解析解 

分 类 号：O357.41[理学—流体力学]