一类双参数弹性地基上正交各向异性矩形薄板弯曲方程的辛方法  

Symplectic Method for a Class of Orthotropic Rectangular Thin Plates Bending Equation on Two Parameters Elastic Foundation

作　　者：江涛 额布日力吐[1] 阿拉坦仓[2] JIANG Tao;Eburilitu;Alatancang(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;Hohhot Minzu College,Hohhot 010051 ,China)

机构地区：[1]内蒙古大学数学科学学院 [2]呼和浩特民族学院

出　　处：《内蒙古大学学报（自然科学版）》2019年第1期11-17,共7页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金项目(11862019;11362011;11761052;11761029)

摘　　要：利用辛方法研究了双参数弹性地基上正交各向异性矩形薄板的弯曲问题,首先计算出原方程在一边简支对边滑支边界条件下对应的Hamilton算子的本征值和本征函数系,并证明了该本征函数系的辛正交性和它的完备性.进而算出双参数弹性地基上一边简支对边滑支正交各向异性矩形薄板弯曲问题的通解.最终,通过一个算例验证了所得通解的正确性.The symplectic method is used to study the bending problems of orthotropic rectangular thin plates on two parameters elastic foundation.First,the eigenvalue and eigenfunction system of Hamiltonian operator corresponding to the original equations with one side simply supported and the opposite side slidingly supported are calculated,and the symplectic orthogonality and completeness of the eigenfunction system are proved.Then,the general solutions to the bending problems of orthotropic rectangular thin plates with one side simply supported and the opposite side slidingly supported on the two parameters elastic foundation are obtained.Finally,an example is given to verify the correctness of the obtained general solution.

关 键 词：双参数弹性地基 正交各向异性矩形板 辛方法 HAMILTON算子 完备性 

分 类 号：O175.3[理学—数学]