基于有限元分析的石墨烯弹性性能和振动特性

Elastic properties and vibration characteristics of graphene using finite element method

为了研究石墨烯的弹性性能和振动特性,采用集中质量单元代替碳原子、矩形梁单元来模拟碳-碳共价键,建立了石墨烯框架结构连续介质模型,并利用有限元方法对模型进行分析.结果表明:弹性性能与手性相关,扶手椅型石墨烯的弹性性能优于锯齿型;随着尺寸的增大,石墨烯逐渐表现出各向同性,其杨氏模量、剪切模量和泊松比分别趋于1.03 TPa,440 GPa和0.175.振动特性不依赖于手性,2种手性石墨烯的固有频率和振型基本一致;固有频率随尺寸的增大而减小,而对应的振型则保持不变;边界条件对固有频率和振型有很大影响,边界的约束越多得到的固有频率越大,且不同边界条件的石墨烯具有完全不同的振型.

In order to study the elastic properties and vibration characteristics of graphene,a frame structure continuum model is developed.The carbon atoms are represented by lumped masses,and C—C covalent bonds are modeled as rectangular beams.Then the continuum model is analysed using finite element method.The results show that the elastic properties of graphene correlate to the chirality,and armchair graphene have better elastic properties.Graphene may gradually become isotropic as the sizes increase.The Young＇s modulus,shear modulus and Poisson＇s ratio of graphene tends to be 1.03TPa,440GPa and 0.175,respectively.The vibration characteristics of graphene do not depend on the chirality.The natural frequencies of graphene decrease with the sizes,but the corresponding mode shapes remain unchanged.The boundary conditions have a great effect on the frequencies and mode shapes.The more the boundary constraints,the higher the natural frequencies of graphene.In addition,graphene with different boundary conditions have completely different mode shapes.