Amin Nasrollahzadeh - Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Pardis St., Mollasadra Ave, Vanak Square, ۱۹۱۹۴۳۳۴۴, Tehran, Iran.
Shayan Rahimi Shahmirzadi - Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Pardis St., Mollasadra Ave, Vanak Square, ۱۹۱۹۴۳۳۴۴, Tehran, Iran.
Ali Najafi Ardekany - Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Pardis St., Mollasadra Ave, Vanak Square, ۱۹۱۹۴۳۳۴۴, Tehran, Iran.

Microtubules consist of strings α and β, which are parallelized in order that a hollow cylinder of nanotubes with an inner and outer diameter of 17 and 25 nm is formed. In this article, free vibrations of microtubule have been studied in functionally graded materials (FGMs) utilizing first-order shear deformation based on the stress gradient and strain gradient elasticity theories. The microtubule has been considered as a cylindrical shell, and because of the inhomogeneous structure of the microtubule due to its non-similar components α and β tubulins, the elasticity modulus will be radially varying. In this article, the Young modulus is varying through the radius, and it will be tunable by changing some of the inhomogeneity constant. Microtubule is an inhomogeneous isotropic material with Young modulus exponentially radially varying and constant Poisson's ratio. The effects of changing the inhomogeneity constant, dimensional ratios, transverse and axial wavenumbers, and longitudinal scale parameters are studied in various shape modes

Gradient elasticity; Functionally graded materials; Tubulin; Free vibrations