一维六方准晶简支梁的自由振动  

Free Vibration of a One-dimensional Hexagonal Quasicrystal Simply Supported Beam

作　　者：赵延军 周彦斌[1] 刘官厅[1] ZHAO Yan-jun;ZHOU Yan-bin;LIU Guan-ting(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《数学的实践与认识》2022年第9期194-200,共7页Mathematics in Practice and Theory

基　　金：内蒙古自然科学基金(2020LH01011);内蒙古师范大学高层次人才引进科研项目资助(2019YJRC005)。

摘　　要：采用不同高阶剪切变形理论研究一维六方准晶梁的自由振动问题,应用哈密顿原理,推导了一维六方准晶梁的自由振动控制微分方程.采用Navier法获得了一维六方准晶简支梁自由振动的精确解,并将不考虑相位子场所求解结果与已有解进行比较,验证求解结果的有效性.最后研究材料尺度对一维六方准晶梁固有频率的影响.The free vibration of one dimensional hexagonal quasicrystal beam is studied by using different high-order shear deformation theory,and the free vibration control differential equation of one dimensional hexagonal quasicrystal beam is derived by using Hamilton principle.The exact solution of free vibration of one-dimensional hexagonal quasicrystal beam is obtained by Navier method.The solution results without considering the phason field are compared with the existing solutions to verify the validity of the solution results.Finally,the effect of material size on the natural frequency of one-dimensional hexagonal quasicrystal is studied.

关 键 词：准晶 剪切变形理论 自由振动 频率 

分 类 号：O753.3[理学—晶体学]