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.

如今，纳米结构脂质载体被用作载体系统来控制药物分子的释放并促进其理化稳定性。更好地了解脂质纳米管的动态行为可以促进更好的药物递送和其他相关应用。这些脂质纳米管的动力学行为容易受到温度变化的影响。因此，如上所述，必须对这些效应进行更深入的了解，以确保更高的分析效率。但是，先前研究中使用的模型并未考虑这些影响。脂质纳米管通常具有较小的长宽比，因此，使用Euler-Bernoulli束理论对它们进行建模会大大降低计算的准确性，其中季莫申科梁模型用于提高模型的准确性。本研究的主要目的是基于非局部应变梯度理论，通过考虑温度效应来研究脂质纳米管的弯曲振动。为此，根据汉密尔顿原理，通过考虑温度效应来提取动力系统的控制方程。使用Navier解法对方程进行求解。此外，计算了脂质纳米管的无量纲固有频率和临界温度。我们的发现表明，临界温度是非局部参数和长度尺度参数变化的函数。还可以观察到，在一定长度的比例尺参数上，增加非局部参数的值会导致脂质纳米管的硬化行为增强。根据我们的发现，所提出的模型显示出良好的准确性和预测性。