Size-dependent thermo-mechanical vibration of lipid supramolecular nano-tubules via nonlocal strain gradient Timoshenko beam theory

Nowadays, nanostructured lipid carriers are used as carrier systems to control the release of drug molecules and promote their physicochemical stability. A better understanding of the dynamic behavior of lipid nano-tubules can facilitate a better drug delivery and other relevant applications. The dynamic behaviors of these lipid nano-tubules are susceptible to temperature variations. Hence, a deeper insight into these effects, as mentioned above, is necessary to ensure higher analysis efficiency. However, the models used in previous researches did not take into account these effects. The lipid nano-tubules often possess a small length-to-width ratio and as a result, the use of the Euler-Bernoulli beam theory for modeling them will significantly reduce the accuracy of calculations, in which Timoshenko beam model is used to increase the accuracy of the model. The main objective of the current study is to investigate the bending vibrations of lipid nano-tubules by considering the temperature effects based on nonlocal strain gradient theory. To this end, based on Hamilton's principle, the governing equations of a dynamical system were extracted by taking into account the temperature effects. The equations were solved using the Navier solution method. Moreover, the dimensionless natural frequency and critical temperature of the lipid nano-tubules were calculated. Our findings demonstrate that the critical temperature is a function of the nonlocal parameter and length-scale parameter variations. It is also observed that at a certain interval of the length scale parameter, increasing the value of the nonlocal parameter results in intensification of the hardening behavior of lipid nano-tubules. Based on our findings, the proposed model indicates good accuracy and prediction.