Nonlinear vibration of microtubules in living cells

Large amplitude flexural vibration behavior is presented for microtubules (MTs) embedded in an elastic matrix of cytoplasm. The microtubule is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effect. The surrounding elastic medium is modeled as a two-parameter elastic foundation. Formulations are based on higher order shear deformation shell theory with a von Kلrmلn-Donnell-type of kinematic nonlinearity. The thermal effect is also included and the material properties are assumed to be temperature-dependent. The small scale parameter e0a is estimated by matching the fundamental frequencies from existing results with the numerical results obtained from the nonlocal shear deformable shell model. The numerical results show that the fundamental frequencies of MTs are very sensitive to the small scale parameter e0a. The results reveal that the small scale parameter e0a reduces the natural frequencies of MTs, but the effect of the small scale parameter on the nonlinear vibration response is relatively weaker when compared to the effect of the small scale parameter on the postbuckling response of MTs.