A solution to free vibration of rotating pretwisted hybrid CNTs multiscale functionally graded conical shell

In the present study, the free vibration analysis of multiscale functionally graded (FG) carbon nanotube (CNT)–metal–ceramic composite conical shells is conducted using finite element methodology. Using first-order shear deformation theory (FSDT) strains are computed and an eight noded isoparametric shell element is used in the present formulation. Dynamic equation is derived using Lagrange's equation of motion for moderate rotational speeds wherein Coriolis effect is neglected. The finite element code is developed and validated with the existing literature to analyze the effects of power law index, weight fraction of CNTs, length to thickness ratio, aspect ratio, twist angle and rotational speeds on fundamental natural frequency. Mode shapes of both twisted and untwisted conical shells under varying rotating conditions are also presented.