Abstract Free vibration of the imitated super carbon nanotube (ISCNT) is studied based on the coarse-grained method together with 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 the carbon nanotubes, the super carbon nanotubes (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 important to its application and thoroughly understanding its mechanical properties. The imitated carbon nanotubes which constructs 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 obtained by 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 finite element method. The coarse-grained method is validated in the vibration behavior analysis of the ISCNT with different sizes. The results show that the increasing of radius of imitated bond and imitated carbon nanotubes leads to the increase of natural frequency of the ISCNT. The increasing of length 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.
Received: 27 November 2019
Published: 28 August 2020
2020, Vol. 41 
