Finite Element Modeling of the Free Vibration Behavior of Reinforced Polymers with Carbon Nanotubes

The free vibration of a representative volume element (RVE) has been studied using finite element approach. The RVE is modeled as two concentric cylinders, the core cylinder is a CNT, which is embedded in the polymeric matrix. The length and thickness of the CNT, the length and diameter of the matrix, and finally the CNT volume fraction are considered as variable parameters in this modeling. The length and thickness of the CNT have considerable effects, in a way that it is not possible to define a cut-off length here. The results show at the constant CNT volume fraction, the natural frequencies decreased with increasing in the length, thickness and diameter of the CNT and increased with decreasing in the diameter of the polymeric matrix. In addition, the natural frequencies decreased with increasing in the CNT volume fraction due to the increasing CNT length.