VIBRATION ANALYSIS OF COUPLED PROTEIN MICROTUBULES BASED ON NONLOCAL EULER-BERNOULLI AND TIMOSHENKO BEAM THEORIES

In the present research, Euler-Bernoulli (EB) and Timoshenko beam (TB) models are developed to investigate vibrational behavior of coupled protein microtubules (MTs). MTs are hollow cylindrical filaments in the eukaryotic cytoskeleton which surrounded by filament network. Bio-medium surrounding the MTs is simulated by Winkler-Riley Model. To enhance the accuracy of results, nonlocal theory is utilized, and the motion equations as well as the boundary conditions are derived based on Hamilton’s principle.Considering surface traction of the cytosol, effects of various parameters such as environmental conditions, aspect ration of MTs and small scale on vibration characteristics of coupled MTs are obtained. Results revealed that stability of coupled MTs are strongly dependent on the ratio of length to radius so that increasing aspect ratio leads to decrease frequency of coupled MTs. The results may provide a useful reference for explaining the main role in the ultrasonic examine of microtubule organization in biomedical clinical application.

Keywords:

Coupled protein microtubules , Euler-Bernoulli beam model , Timoshenko beam model , Nonlocal theory