黏弹性地基上石墨烯增强功能梯度矩形板的自由振动和动力响应  

Free vibration and dynamic response of functionally graded graphene-reinforced rectangular plates on viscoelastic foundations

作　　者：黄小林 魏耿忠 刘思奇 钟德月 Huang Xiaolin;Wei Gengzhong;Liu Siqi;Zhong Deyue(School of Architecture and Transportation Engineering,Guilin University of Electronic Technology,541004,Guilin,China)

机构地区：[1]桂林电子科技大学建筑与交通工程学院,桂林541004

出　　处：《应用力学学报》2021年第3期1202-1208,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11362004)。

摘　　要：考虑黏弹性地基的影响,基于复合材料薄板理论建立了石墨烯增强功能梯度矩形薄板的运动方程,用Galerkin法和龙格库塔法求解其自振频率和动力响应,分析了地基参数、石墨烯含量和分布对自振频率和动力响应的影响。结果表明:黏弹性地基的剪切和压缩刚度提高了板的自振频率,减小了动力响应;地基黏性降低了板的自振频率和动力响应;在石墨烯纳米片的四种分布模式中,在板的顶部和底部埋置更多的石墨烯是减小动力响应的最有效模式。Based on the three-parameter model of viscoelastic foundation and composite thin plate theory,the equations of motion for functionally graded graphene-reinforced rectangular plates on viscoelastic foundations are established.The solutions of the free vibrations and dynamic responses for the plates are obtained by using Galerkin method and Runge-Kuta technique.The effects of foundation parameters,distribution patterns and weight fraction of graphene nanoplatelets on the natural frequencies and dynamic responses are investigated.The results reveal that the natural frequencies rise with the increase of the weight fraction of graphene nanoplatelets,the compression and shear foundation parameters.The central transient deflections of the plates decrease as the weight fraction of graphene nanoplatelets,the compression and shear foundation parameters increase.Among the four distribution modes of graphene nanoplatelets,dispersing more graphene nanoplatelets into the top and bottom surfaces is the most effective way to reduce dynamic responses.

关 键 词：石墨烯 功能梯度材料 黏弹性地基 矩形板 振动 

分 类 号：O327[理学—一般力学与力学基础]