一块简支石墨烯片动力响应的小尺度效应研究  

Small scale effect of a simply supported graphene sheet's dynamic response

作　　者：谢根全[1] 王建平[2] 张琦珑 XIE Genquan1 ,WANG Jianping2 , ZHANG Qilong1(1. School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, China; 2. Mianyang Polytechnic, Mianyang 621000, Chin)

机构地区：[1]湖南科技大学土木工程学院,湖南湘潭411201 [2]绵阳职业技术学院,四川绵阳621000

出　　处：《振动与冲击》2018年第15期277-282,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(11372109)

摘　　要：对一块简支石墨烯片动力响应的小尺度效应进行了研究,基于非局部弹性力学的概念和能量法建立了简支石墨烯片的动力响应微分方程。通过求解这个微分方程得到简支石墨烯片的动挠度,定义基于经典理论的石墨烯片中心点动挠度最大值和基于非局部理论的石墨烯片中心点动挠度最大值之比为小尺度效应因子。计算了不同频率激励下,不同长宽以及不同螺旋角的石墨烯片的小尺度因子,数值结果表明,石墨烯片的螺旋角、小尺寸和激励频率对它的动挠度的小尺度效应有影响,当石墨烯片的长度和宽度都大于1 mm时,它的动力响应的小尺度效应消失。Small scale effect of a simply supported graphene sheet＇s dynamic response was investigated. Dynamic differential equation of the graphene sheet was built based on the concept of the nonlocal elastic mechanics and the energy method. Dynamic deflection of the simply supported graphene sheet was obtained by solving the dynamic differential equation. The small scale effect factor was defined as the ratio of the maximum dynamic deflection of the graphene sheet＇s center point based on the classical theory to one based on the nonlocal theory. Small scale effect factor was calculated for a graphene sheet with different lengths,widths and helical angles under excitations of different frequencies. The numerical results showed that the small scale effect of a graphene sheet＇s dynamic deflection is affected by the sheet＇s small size,helical angle and excitation frequency; when the length and the width of the graphene sheet are both larger than 1 mm,its dynamic response＇s small scale effect disappears.

关 键 词：非局部理论 简支石墨烯片 小尺度效应 动挠度 螺旋角 

分 类 号：O369[理学—流体力学]