Nonlocal orthotropic shell model applied on wave propagation in microtubules

•Wave velocity formulas in microtubules are obtained with nonlocal shell model.•The results are explained both in mathematics and physics.•The stability of wave at higher and lower temperature is found.

Wave propagation in microtubules is investigated based on the nonlocal elastic theory. The complete analytical formulas of wave velocity are obtained, and the results demonstrate that the small scale effect can reduce the velocity, especially for large longitudinal wave-vector and large circumferential wave number. When the wave length is smaller than 80 nm, the small scale effects are more significant. The results match the conclusions of lattice vibration well. Besides, temperature is taken into account and the results show that the temperature effect on waves in microtubules is not monotonous but have a certain stableness in higher and lower temperature zone. The methods and results may also support the design and application of nano devices such as micro sound generator etc.