Effect of the aspect ratio and waviness of carbon nanotubes on the vibrational behavior of functionally graded nanocomposite cylindrical panels

In this study, based on the three‐dimensional theory of elasticity, free vibration characteristics of nanocomposite cylindrical panels reinforced by single‐walled carbon nanotubes (CNTs) are considered. The carbon nanotube‐reinforced (CNTRC) cylindrical panel has smooth variation of CNT fraction in the radial direction, and the material properties are estimated by the extended rule of mixture. In this work, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube‐to‐tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Symmetric and asymmetric volume fraction profiles are provided in this work for comparison. Suitable displacement functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the equilibrium equations to a set of coupled ordinary differential equation with variable coefficients, which can be solved by a generalized differential quadrature method. The results show that the kind of distribution and volume fraction of CNT have a significant effect on normalized natural frequency.POLYM. COMPOS., 33:2036–2044, 2012.