Theoretical study of the effect of shear deformable shell model, elastic foundation and size dependency on the vibration of protein microtubule

In this paper, isotropic cylindrical shell model with first order shear deformation theory based on modified couple stress theory is used to investigate the mechanical behavior of microtubules and to consider the size effect in the nano-scale. Besides, partial equations of shell motion with classical and non-classical corresponding boundary conditions are derived from Hamilton's principle. The study models the microtubule as a simply supported shell and the Navier procedure is used to solve the vibration problem. To simulate the environment of microtubule, Pasternak foundation is used. The free vibration of the microtubule is examined in the presence and absence of cytoplasm, and the significant parameter, length dependence flexural rigidity is determined based on the new model. Finally, the effect of different system parameters such as length, size effect parameters, shear modulus ratio and substrate parameters on free vibration microtubule is investigated. Comparison of the results of the new model with the classical model and the results obtained by other researchers reveals that the model presented in this paper is more accurate than other models used in this area and in better agreement with experimental data. (C) 2015 Elsevier Ltd. All rights reserved.