Three-Dimensional Free Vibration Analysis of Carbon Nanotube Reinforced Composites Annular Plates

The main objective of this research work was to investigate three-dimensional free vibration of thick annular plates which are composed of carbon nanotube (CNT) reinforced composites materials using the Chebyshev–Ritz method. In order to obtain precise results, a new form of the rule of mixtures including an exponential shape function, length efficiency parameter, orientation efficiency factor, and waviness parameter was applied for predicting the mechanical properties of CNT reinforced composites. Convergence of the Chebyshev–Ritz method was also checked. Numerical results are given and compared with the available literature and finite element method (FEM) analysis. Results obtained from the other well-known theories (such as: Micro-Mechanical, Halpin, etc.) are compared with the new form of the rule of mixtures results. Furthermore, the effects of CNT type, structures, diameter, shape factor, density, and volume fraction on the vibration behavior of the annular plates are graphically presented.