A solution for free vibration of rotating hybrid multiscale nanocomposite conical shell

In the present investigation, first-order shear deformation theory (FSDT) is employed to conduct free vibration analysis of hybrid CNT-fiber nanocomposite conical shells using finite element approach. The effective material properties of this three phase nanocomposite is computed using Halpin- Tsai and Micro-mechanics model approach. The Lagrange’s equation of motion is used to derive the equilibrium equations of the rotating carbon nanotube – fibre nanocomposite conical shell wherein the nonlinearity due to rotation is also introduced. The Coriolis effect is neglected because of the moderate rotational speed of the shell. Finite element code is developed using eight noded isoparametric shell element and the same is validated with some literature to analyse the effect of twist angle, length to thickness ratio, aspect ratio, weight fraction of CNTs, and rotational speed on the fundamental frequency. The effect of such parameter on the mode shapes of the three phase nanocomposite shell are also presented here.