Vibration of microtubules as orthotropic elastic shells

In view of the fact that shear modulus and circumferential modulus of microtubules are more than one order of magnitude lower than longitudinal modulus, an orthotropic elastic shell model for microtubules is developed, for the first time in the literature, to study vibration behavior of microtubules. The suggested model is justified by a good agreement between the results given by the present model and some available known data in a few special cases. Further, the model is used to study general behavior of free vibration of microtubules. Consistent with some known results, the present results show that isotropic model substantially overestimates vibrational frequencies of almost all modes except axisymmetric longitudinal modes and beam-like bending modes. In particular, the isotropic model overestimates frequencies of torsional modes by even more than one order of magnitude. In addition, radius dependency of frequency of axisymmetric radial modes is examined. It is believed that the present model offers a simple and effective new approach to study mechanical behavior of microtubules.