功能梯度石墨烯增强复合材料板的自由振动  

Free vibration of functionally graded graphene-reinforced composite plates

作　　者：庞有卿 王爱文[1,2] 郝育新 陈鸿燕[1] Pang Youqing;Wang Aiwen;Hao Yuxin;Chen Hongyan(School of Applied Science,Beijing Information Science and Technology University,100192,Beijing,China;Department of Mechanical and Electronic Engineering,Beijing University of Technology,100022,Beijing,China;Department of Mechanical and Electronic Engineering,Beijing Information Science and Technology University,100192,Beijing,China)

机构地区：[1]北京信息科技大学理学院,北京100192 [2]北京工业大学机电工程学院,北京100022 [3]北京信息科技大学机电工程学院,北京100192

出　　处：《应用力学学报》2020年第2期558-565,I0006,I0007,共10页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11772063,11472056,11290152,11427801,11502165)。

摘　　要：基于高阶函数剪切变形板理论,研究了可移动简支边界条件下功能梯度石墨烯增强复合材料板的自由振动。利用修正的Halpin-Tsai模型估计了复合材料的等效杨氏模量。基于Hamilton原理构建其偏微分方程。通过Navier方法计算得到了板的量纲为一的频率,并与已有成果进行了比较,验证了本文计算模型的优越性。数值计算结果表明:功能梯度石墨烯增强复合材料板的量纲为一的基频受石墨烯小块的分布模式影响很大,随着石墨烯含量的增加而单调增加;固定石墨烯小块的厚度和长宽比,量纲为一的基频随着长厚比的增加而单调增加。Free vibration of a simply supported functionally graded graphene-reinforced composite plate is presented based on a general higher order shear deformation theory.The effective Young’s modulus is estimated bya modified Halpin-Tsai model.The dynamics model is obtained according to the Hamilton’s principle.The dimensionless frequencies of functionally graded graphene-reinforced composite plate are calculated by Navier method and compared with the results in the literatures available.The superiority of the calculation results in this paper and the convergence with the increase of total number of layers are verified.Numerical results obtained show that the dimensionless fundamental frequencies of a functionally graded graphene-reinforced composite plate is greatly influenced by the distribution pattern of graphene nanoplatelets,and increase monotonously with the increase of graphene weight fraction.The dimensionless fundamental frequencies increase monotonously with the increase of the length-to-thickness ratio with the fixed thickness and aspect ratio of graphene nanoplatelets.

关 键 词：功能梯度 石墨烯增强复合材料 高阶剪切变形理论 自由振动 

分 类 号：TB34[一般工业技术—材料科学与工程]