Abstract
A biomechanical model for vibrational analysis with characteristics of protein microtubules based on the nanobeam shape inside the cellular structure is presented. Young's modulus of protein microtubules and unexplained length-dependent flexural rigidity are studied using a higher-order nonlocal shear deformation theory. The governing equations are provided by employing the principle of virtual work. The protein microtubules are considered simply supported for all numerical studies. The obtained results are critically discussed together with the theories as well as demonstrated in each case graphically.