Using a New Size Dependent Orthotropic Elastic Shell Model for the Investigation of Free Vibration of Protein Microtubules

Protein microtubules are one of the most effective intracellular components. The microtubules structure is in a manner that their behaviour is similar to that of the orthotropic materials. Therefore, in this paper, size-dependent vibration of the anisotropic protein microtubule is studied. For this purpose, using a first shear deformable shell model and based on couple stress theory, new equations are developed for the dynamic behavior of anisotropic protein microtubule. After solving the governing equations of microtubule motion, the effects of cytoplasm environment, microtubule dimensions and its mechanical properties, and material length scale parameters on the natural frequency of microtubules are investigated.