Vibrational response of coupled orthotropic protein microtubules immersed in cytosol considering small-scale and surface effects

In this research, orthotropic Euler–Bernoulli beam and Timoshenko beam models are developed to investigate vibrational behavior of coupled protein microtubules. Microtubules are hollow cylindrical filaments in the living cells which are surrounded by filament network, which is simulated by Winkler–Riley Model. Temperature-dependent material properties for microtubules are used to study the thermal effect on vibration frequency. To apply the size effect, nonlocal theory is utilized, and the motion equations are derived based on Hamilton’s principle. In order to examine reliability of presented study, effects of various parameters such as environmental conditions, temperature change, boundary conditions and small-scale parameters on vibration characteristics of isotropic and orthotropic microtubules for both Euler–Bernoulli beam and Timoshenko beam models are discussed in detail. Results revealed that dynamic behavior of coupled microtubules is strongly dependent on the surface elasticity modulus of cytosol, so that, increasing surface elasticity modulus leads to increase in frequency of coupled microtubules. Results of this investigation can be provided as a useful reference in bio-medical clinical application.