FREE VIBRATION OF MICROTUBULES AS ELASTIC SHELL MODEL BASED ON MODIFIED COUPLE STRESS THEORY

Abstract

In this study, first, the thin cylindrical shell theory was derived from the modified couple stress theory and, afterwards, the vibration of protein microtubules (MTs) was investigated using the developed model. In order to model protein MTs more precisely, the cylindrical micro-shell model was used. Also, to take account of small size effects, equations of motion were obtained on the basis of the modified couple stress theory. For this purpose, first, using Hamilton's principle, vibration equations of cylindrical shell with boundary conditions were derived from the modified couple stress theory. Finally, the effects of size parameters, MT dimensions, and the medium surrounding on the axial and circumferential vibration frequency of the MT were examined. It should be noted that the results obtained from the cylindrical micro-shell model, unlike those from the beam model, have lower dependency on MT length, but they have extreme dependency on MT thickness and radius. In the end, it is worth noting that the model developed in this study can predict experimental results with greater precision compared to classic models. In other words, this model narrows the gap existing between experimental results and previous models and theories.