均布载荷作用下十次对称二维准晶梁的辛解析法  

Symplectic Analytical Method of Decagonal Quasicrystal Beam Under Uniformly Distributed Load

作　　者：李光芳 范俊杰 LI Guang-fang;FAN Jun-jie(College of Science,Inner Mongolia Agricultural University,Hohhot 010018,China;Inner Mongolia Center for Applied Mathmatics,Hohhot 010022,China;Honder College of Arts and Sciences Inner Mongolia,Hohhot 010000,China)

机构地区：[1]内蒙古农业大学理学院,内蒙古呼和浩特010018 [2]内蒙古自治区应用数学中心,内蒙古呼和浩特010022 [3]内蒙古鸿德文理学院,内蒙古呼和浩特010000

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2023年第1期73-80,共8页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11962026,12002175,12162027,62161045);内蒙古自治区自然科学基金资助项目(2020MS01018,2021MS01013,2022ZD05);内蒙古自治区高等学校科学技术研究资助项目(NJZY22519);内蒙古师范大学基本科研业务费资助项目(2022JBZD010);内蒙古农业大学基础学科科研启动基金资助项目(JC2020002)。

摘　　要：基于十次准晶弹性力学的基本方程,给出十次准晶梁Hamilton对偶方程。利用分离变量法获得了侧边为齐次边界条件的平面问题的基本解,并将求解方法推广到非齐次边界条件情形,进而给出了通解的一般表达式。在此基础上,讨论了受均布载荷的十次对称二维准晶悬臂梁问题,依据边界条件确定了通解中的待定系数,得到了声子场和相位子场应力和位移的解析表达式。The Hamilton dual equation of decagonal quasicrystal beam is derived based on the basic equation of decagonal quasicrystal elasticity. The basic solution of the plane problem with homogeneous boundary conditions is obtained by using variable separation method. Then, the method is applied to the case of non-homogeneous boundary conditions, and the expression of the general solution is thereupon given. On this basis, the problem of decagonal quasicrystal cantilever beam under uniformly distributed load is discussed.According to the boundary conditions, the undetermined coefficients in the general solution are determined and the analytical expressions of stress and displacement of phonon field and phase field are obtained.

关 键 词：Hamilton对偶方程 准晶 悬臂梁 解析解 

分 类 号：O29[理学—应用数学]