Investigating the nonlinear free vibrations of Nanocomposite beam based on multiscale modeling

The main aim of this paper is to investigate the nonlinear free transverse vibration of representative volume element (RVE) of nanocomposites based on multiscale method, in order to predict the vibration behavior of nanocomposite beam at macro scale. To reach this object, first, mechanical properties of volume element containing carbon nanotube (CNT) is determined. In this regard, various RVEs with different length ratios are considered, where each of them represents a kind of distribution in the nanocomposite environment. Then with finite element modeling and analytical solutions, in linear domain, modal analysis of CNTs and RVEs are investigated. The results indicate that the higher ratio of nanotubes, which represents the uniform distribution of the nanotubes in the resin, has a higher natural frequency. Also, the results of analytical solution have shown good agreement with the FE modeling. In order to further validate the results of modal analysis is performed on CNT and compared with previous studies. Then, the vibration equations of volume element based on the Von-Kármán theory are obtained and nonlinear free vibration behavior of RVEs are investigated in different boundary conditions. The nonlinear frequency of volume element as a function of vibration amplitude showed that the boundary conditions and dispersion state of CNTs have a great effect on the rate of the system nonlinear behavior. Results indicate that in clamp-pinned condition the nonlinear frequency rate is approximately 20% more than clamp-clamp condition and also the values of frequency increase by improving the dispersion state of system.