基于粗粒化方法的类超级碳纳米管自由振动研究

Free Vibration of Imitated Super Carbon Nanotubes Based on the Coarse-grained Method

超级碳纳米管是在碳纳米管结构基础上,将每一根碳-碳键替换为碳纳米管而形成的新型结构.类超级碳纳米管是超级碳纳米管对应的宏观结构,在保持外观结构的基础上将尺度放大到宏观尺度.论文建立了类超级碳纳米管的粗粒化模型.基于粗粒化方法,研究了类超级碳纳米管的自由振动.分析了内外管半径以及长度对类超级碳纳米管振动行为的影响.与原结构有限元进行对比,结果表明粗粒化方法能有效的计算类超级碳纳米管的振动行为.

Free vibration of the imitated super carbon nanotube(ISCNT) is studied based on the coarse-grained method together with the finite element method of the original structure of the ISCNT. The carbon nanotubes have many excellent mechanical and electrical properties. Based on the structure of carbon nanotubes, the super carbon nanotube(SCNT) is a new type of structure, replacing each carbon-carbon bond with carbon nanotubes. The ISCNT is the corresponding macro structure of SCNT which keeps the exterior structure of the SCNT and enlarges the scale to the macro scale. The vibration behavior of ISCNT is of importance for its application and a thorough understanding of its mechanical properties. The imitated carbon nanotubes which construct the ISCNT are equivalent to Euler beams to build the coarse-grained model of the ISCNT. The coarse-grained method based on the equivalent Euler beam element is presented to investigate the free vibration of the ISCNT. The effective bending Young’s modulus of the equivalent Euler beam can be obtained by the first-order natural frequency from the finite element calculation of the original structure of imitated carbon nanotubes. The Poisson’s ratio of the equivalent Euler beam can be obtained by the stretching of the original structure of imitated carbon nanotubes via the finite element method. The coarse-grained method is validated in the vibration behavior analysis of the ISCNT with different sizes. The results show that increasing the radius of imitated bond and imitated carbon nanotubes leads to the increase of natural frequency of the ISCNT. Increasing of the lengths of imitated carbon nanotubes and the ISCNT leads to the decrease of natural frequency of the ISCNT. The results show that the coarse-grained method can be effectively used to study the free vibration of ISCNT, so as to save time in building ISCNT models and calculating the vibration behavior of the ISCNT.