Free vibration analysis of microtubules based on an atomistic-continuum model

Abstract Analysis of free vibration of microtubules, based on an atomistic-continuum model, is presented. The theory bridges the polyatomic structure of microtubules with a macroscopic continuum approach under mesh-free computing scheme. A higher-order gradient continuum constitutive relationship is developed and incorporated into a higher-order Cauchy–Born rule. Instead of considering the atomic interaction between every atom pair in such polyatomic bio-composite textures, interatomic energy between subcomponents in microtubules is evaluated by a homogenization technique, represented by the fictitious bond. Material properties and stiffness matrix are determined, depending on deformation of fictitious bonds. Since the mesh-free approximation automatically satisfies the higher-order continuity and possesses intrinsic nonlocal property, the established quasicontinuum theory takes into consideration both atomic interaction and the size effect for modeling this microscale structure. Natural vibration frequencies of microtubules of different lengths and boundary restrictions are predicted and compared with existing solutions.