Scale-Dependent Thermomechanical-Forced Noncircular Torsional Vibration of Lipid Supramolecular Nanotubes via Timoshenko–Gere Theory

Abstract

Dynamic modeling of lipid nanotubes as a drug carrier in the skin layer is important. The displacement fields of lipid nanotubes in the shunt path of the skin layer are considered twisting. The twisting of the lipid nanotube in the skin layer causes the warping of the structure and, as a result, causes normal strain. The normal strain in the strain fields is not considered in the torsional noncircular structures. Therefore, in this study, not only the effect of shear strains but also the effect of normal strain on the torsional vibration of lipid nanotubes are considered based on the Timoshenko–Gere theory for the first time. Also, the temperature can be considered in the modeling due to the normal strain in the torsional of warped structures. Then, the governing equations of the forced torsional vibrations of lipid nanotubes, by considering the general warping function of cross-section, are derived based on the nonlocal strain gradient theory. The governing equation is solved by utilizing the convolution integration, and the dynamic responses of lipid nanotubes in the presence of external nonlinear harmonic moving torque are obtained. In the results, dynamic and frequency responses in the presence of temperature for rectangular and elliptical lipid nanotubes have been analyzed. One of the methods of drug release in nanocarriers is stimulation with ultrasound waves. Therefore, stimulating the lipid nanotubes using ultrasound waves at the obtained frequencies makes it possible to release the drug from the lipid nanotubes. Also, the maximum dynamical response of Timoshenko–Gere torsion is less than typical torsion. Increasing the aspect ratio of cross-section dimensions of lipid nanotubes decreased the maximum dynamical response. Increasing the velocity parameter first increases the dynamical twist and then reduces it. Also, the effects of axial forces and temperature on the maximum dynamical responses and the dynamical twist of the lipid nanotubes are studied. For validation, the obtained results are compared with the results of previous research.