Wave propagation induced by body forces for free microtubules using cylindrical shell model

This paper examines the wave velocity of protein microtubules using a elasticity model that incorporates body forces, based on the structure of these hollow cylinder-like structures., the governing equations are analytically solved to determine how the body forces effect the wave velocity. To analyze the microtubule waves velocity, use microtubules with simply supported ends. The electric field of a dipole vibrating at the same frequency as microtubule vibrations approximates the electric field generated by the rhythmic motion of every charge. The numerical findings for the three modes of frequencies in the longitudinal, radial, and torsional directions for the current conditions are compared with the results of previous calculations.