含孔功能梯度板的动力学分析  

Dynamics of Functionally Graded Plates with a Hole

作　　者：娄光路 随岁寒 孟华[1] LOU Guang-lu;SUI Sui-han;MENG Hua(School of Mechanical Engineering,Shangqiu Institute of Technology,Shangqiu 476000,Henan,China;Suzhou Juye Information Technology Co.LTD,Suzhou 215000,Jiangsu,China)

机构地区：[1]商丘工学院机械工程学院,河南商丘476000 [2]苏州聚悦信息科技有限公司,江苏苏州215100

出　　处：《兰州文理学院学报（自然科学版）》2023年第5期43-46,51,共5页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：国家自然科学基金(11972240);河南省高等学校重点科研项目(23B130002)。

摘　　要：假设材料由陶瓷和钢做成,材料特性沿着板的厚度方向按照幂指数形式连续变化.基于Kirchhoff薄板理论,结合虚功原理建立含孔功能梯度板的动力学有限元方程.在四边固支的边界条件下,求解得到系统前两阶固有频率,纯钢板和纯陶瓷板条件下与ANSYS方法对比,证明所建模型的有效性,随后探讨了材料梯度指数对前两阶固有频率的影响.结果表明梯度指数增大使得前两阶固有频率减小,趋势逐渐放缓.Suppose the material was made of ceramic and steel,the material characteristics would be continuously changed in the direction of the thickness of the plate according to a power index law.Based on Kirchhoff thin plate theory and virtual work principle,the dynamic finite element equation of functionally gradient plate with holes was established.The first two order natural frequencies of the system were obtained under the boundary condition of four fixed edges.The model established in this paper was proved to be effective by comparing the solution with the ANSYS solution under the condition of pure steel plate and pure ceramic plate.Then,the influence of material gradient index on the first two order natural frequencies was discussed.The results showed that the increase of gradient index maked the first two natural frequencies decrease and the trend gradually slowed down.

关 键 词：含孔 功能梯度板 自由振动 有限元法 

分 类 号：O343[理学—固体力学]