Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory
Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory
复制标题
DOI：
10.1063/1.3091292
复制
发表时间：
2009-03-15
影响因子：
3.2
通讯作者：
Pradhan, S. C.
中科院分区：
文献类型：
--
作者：
Murmu, T.;Pradhan, S. C.
本文采用非局部弹性理论研究了单层石墨烯片的振动响应。非局部弹性理论在处理纳米结构时考虑了小尺寸效应。研究了周围弹性介质对SLGS基频的影响。文克尔型和Pasternak型模型都被用来模拟石墨烯片与周围弹性介质的相互作用。根据汉密尔顿原理，导出了上述问题的控制微分方程.通过本构关系将非局部小尺度系数引入到非局部理论中。采用微分求积法，得到了频率的数值解。数值结果表明，SLGS的基频强烈依赖于小尺度系数。此外，观察到的SLGS与较大的非局部效应和“温克勒型建模”周围介质的非线性频率响应。
In the present work, nonlocal elasticity theory has been implemented to study the vibration response of single-layered graphene (SLGS) sheets. The nonlocal elasticity theory accounts for the small size effects when dealing with nanostructures. Influence of the surrounding elastic medium on the fundamental frequencies of the SLGS is investigated. Both Winkler-type and Pasternak-type models are employed to simulate the interaction of the graphene sheets with a surrounding elastic medium. On the basis of Hamilton's principle governing differential equations for the aforementioned problems are derived. The nonlocal small scale coefficients get introduced into the nonlocal theory through the constitutive relations. Differential quadrature method is being employed and numerical solutions for the frequencies are obtained. Numerical results show that the fundamental frequencies of SLGS are strongly dependent on the small scale coefficients. Further, a nonlinear frequency response is observed for the SLGS with larger nonlocal effects and "Winkler-type modeled" surrounding medium.