Vibration analysis of functionally graded nanocomposite cylinders reinforced by wavy carbon nanotube based on mesh-free method

This work reports the effect of nanotube aspect ratio on the free vibration characteristics of a functionally graded nanocomposite cylinders reinforced by wavy single-walled carbon nanotubes (CNTs) based on mesh-free method. In this simulation, an axisymmetric model is used and axisymmetric natural frequencies of CNT reinforced composite cylinders are presented. The material properties of functionally graded CNT reinforced composites are assumed to be graded in the thickness direction and are estimated by a micromechanical model. The effect of the waviness of the CNTs and its parameters are studied. In the mesh-free analysis, moving least squares shape functions are used for approximation of displacement field in the weak form of motion equation, and the transformation method is used for the imposition of essential boundary conditions. It is observed that the waviness significantly reduces the effective reinforcement of the nanocomposites. The effective moduli and frequency response are very sensitive to the waviness but this sensitivity decreases with the increase of the waviness. The validity of the Young's modulus and the frequency response were assessed by a comparison with available literature data, providing a good agreement.