基于物理中面和Levinson三阶理论FGM圆板固有频率  

Natural frequency of FGM circular plate based on physical neutral surface and Levinson’s third order theory

作　　者：陈宇 李清禄[1] 张靖华[1] CHEN Yu;LI Qing-lu;ZHANG Jing-hua(School of Science,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《复合材料科学与工程》2022年第4期11-17,共7页Composites Science and Engineering

基　　金：国家自然科学基金项目(12062010)。

摘　　要：基于Levinson三阶剪切理论,利用微分求积法研究了功能梯度材料(FGM)圆板的自由振动问题。假设功能梯度材料性质只沿板厚度方向,推导出了问题的控制微分方程,然后利用物理中面的概念,消除了由于材料的横向非均匀性引起的本构方程中拉-弯曲耦合效应,从而使原本非常复杂的控制方程得以简化。用微分求积法(DQM)获得了FGM圆板横向振动的无量纲频率,并与一阶剪切理论下FGM圆板的固有频率进行了比较。通过算例说明了DQM法求解三阶剪切理论FGM圆板的有效性,丰富了Levinson三阶剪切理论的研究成果。数值结果表明:对固支FGM圆板,一阶剪切理论解略微高于Levinson三阶剪切理论给出的解答,而简支FGM板的情况则相反。在此基础上,本文详细讨论了材料梯度指数等各种因素对FGM复合材料圆板固有频率的影响。Based on Levinson’ s third-order shear theory,the free vibration of functionally graded material( FGM) circular plates was studied by differential quadrature method. Assuming that the properties of FGM were only along the thickness direction of the plate,the governing differential equation of the problem was derived. Then,by using the concept of physical midplane,the tension bending coupling effect in the constitutive equation caused by the transverse non-uniformity of the material was eliminated,simplifying the original complex governing equation.The dimensionless frequency of transverse vibration of FGM circular plate was obtained by DQM,and compared with the natural frequency of FGM circular plate under the first-order shear theory. The effectiveness of DQM method in solving FGM circular plates based on third-order shear theory was illustrated by an example,which enriches the research results of Levinson’s third-order shear theory. The numerical results show that the solution of the first-order shear theory is slightly higher than that of Levinson’s third-order shear theory for clamped FGM circular plates,but the opposite is true for simply supported FGM circular plates. On this basis,the effects of various factors such as material gradient index on the natural frequencies of FGM composite circular plates are discussed in detail.

关 键 词：功能梯度材料 Levinson剪切理论 物理中面 自由振动 微分求积法 复合材料 

分 类 号：TB332[一般工业技术—材料科学与工程]