对边简支十次对称二维准晶板弯曲问题的辛分析  

Symplectic Analysis on the Bending Problem of Decagonal Symmetric 2D Quasicrystal Plates With 2 Opposite Edges Simply Supported

作　　者：范俊杰[1,2,3] 李联和 阿拉坦仓[1,2,3] FAN Junjie;LI Lianhe;ALATANCANG(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,P.R.China;Center for Applied Mathematics Inner Mongolia,Hohhot 010022,P.R.China;Key Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application,Ministry of Education,Hohhot 010022,P.R.China)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022 [2]内蒙古自治区应用数学中心,呼和浩特010022 [3]无穷维哈密顿系统及其算法应用教育部重点实验室,呼和浩特010022

出　　处：《应用数学和力学》2023年第7期834-846,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(11962026,12002175,12162027,62161045);内蒙古自然科学基金项目(2020MS-01018,2021MS01013,2022ZD05,2023QN01007);内蒙古自治区高等学校科学技术研究项目(NJZY22519)。

摘　　要：该文讨论了对边简支十次对称二维准晶中厚板弹性问题的辛方法.将十次对称二维准晶弹性理论基本方程转化为Hamilton对偶方程,采用分离变量方法,获得了相应Hamilton算子矩阵的辛特征值及辛特征函数系.证明了Hamilton算子矩阵的辛特征函数系在Cauchy主值意义下的完备性,在此基础上,基于Hamilton系统的辛特征函数展开,给出了十次对称二维准晶板弯曲问题的解析表达式.The symplectic method for the elastic problem of decagonal symmetric 2D quasicrystal plates with 2 opposite edges simply supported,was discussed.The basic equations of the elastic theory for decagonal symmetric 2D quasicrystals were transformed into the Hamilton dual equations.With the method of separation of variables,the symplectic eigenvalues of the corresponding Hamilton operator matrix and the symplectic eigenfunction system were obtained.The completeness of the symplectic eigenfunction system of the Hamilton operator matrix in the sense of the Cauchy principal value was proved.Based on the symplectic eigenfunction expansion of the Hamilton system,the analytical solution to the bending problem of the decagonal symmetric 2D quasicrystal plate was given.

关 键 词：十次对称二维准晶 辛方法 HAMILTON正则方程 完备性 

分 类 号：O343[理学—固体力学]