Nonlocal elasticity effect on vibration characteristics of protein microtubules

For various cellular functions of microtubules (MTs), vibration of microtubules is one of the issues of major concern. In this paper, the vibration characteristics of protein microtubules (MTs) are examined based on a nonlocal Timoshenko beam model and using the wave propagation approach. The small scale effect on MTs wave propagation dispersion relation is explicitly revealed for different MTs wave numbers by theoretical analyses and numerical simulations. The research work reveals the significance of the effects of small scale, transverse shear deformation and rotary inertia on vibrations characteristics of protein microtubules. It is believed that the present model offers a simple and effective new approach to studying vibration characteristics of microtubules.