Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models

In this paper, the size-effects in the torsional and axial response of microtubules by using the nonlocal continuum rod model is investigated. To this end, continuous and discrete rod models are performed for modeling of microtubules. A simple finite element procedure is used for modeling and solution of nonlocal discrete system equation for microtubules. The influence of the small length scale on the vibration frequencies is examined both torsional and axial vibration cases. Some parametric results are also presented for examination of the accuracy and performances of discrete and continuous models.