Free Vibration Analysis of Carbon Fiber-Carbon Nanotube-Polymer Matrix Composite Plates by a Finite Element-Based Multi-Scale Modeling Approach

The vibrational behavior of polymer matrix nanocomposite plates reinforced with carbon fibers (CFs) and carbon nanotubes (CNTs) is studied using the finite element method based on a multi-scale modeling approach. The influences of nano- and micro-scale are coupled through a two-step procedure. First, CNTs are dispersed into the polymer matrix. In the selected representative volume element (RVE), interphase due to chemical interaction between CNT and polymer matrix is considered. Also, the state of dispersion of CNTs into the matrix is assumed to be random. In the second step, CFs are randomly distributed in the reinforced polymer with CNTs. The reinforcement is carried out for various volume fractions of CFs and CNTs. Two three-dimensional models including the brick and shell ones are used to generate the results. Moreover, the analysis is presented for square plates under different types of boundary conditions. The effect of nanocomposite thickness on its vibrational response is also investigated.