On modeling wave dispersion characteristics of protein lipid nanotubules

In this article, wave propagation characteristics of protein lipid nanotubules are covered with respect to scale effects utilizing nonlocal strain gradient theory. The structure is supposed to be modeled as a simply supported beam and the kinematic relations are derived based on the classical beam theory (CBT). Implementing an energy based approach, the Euler-Lagrange equations of the lipid tubules are obtained. Moreover, the final governing equations are solved analytically to achieve the wave frequency and phase velocity of propagated waves. Influences of small size and wave number on the wave dispersion responses of lipid nanotubules are shown in detail in different diagrams for both phase velocity and wave frequency. Also, accuracy of introduced model is verified comparing responses of present model with those of former papers.