Sahmani S, Aghdam M M
Department of Mechanical Engineering, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iran.
Department of Mechanical Engineering, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iran.
J Biomech. 2017 Dec 8;65:49-60. doi: 10.1016/j.jbiomech.2017.09.033. Epub 2017 Oct 9.
The unique geometry with high surface ratio makes lipid micro/nano-tubules as an excellent self-assembled supramolecular structure in various biological applications such as controllable release systems and drug delivery. In the present study, the size-dependent nonlinear vibrations of axially loaded lipid micro/nano tubules associated with the both prebuckling and postbuckling domains are explored comprehensively. To accomplish this purpose, the nonlocal strain gradient theory of elasticity including simultaneously two entirely different features of size dependency is utilized within the framework of the third-order shear deformable beam model. With the aid of Hamilton's principle, the non-classical governing differential equations of motion are established incorporating the nonlinear prebuckling deformations and the large postbuckling deflections. At the end, the Galerkin method in conjunction with an improved perturbation technique is employed to initiate explicit analytical expressions for nonlocal strain gradient nonlinear frequency of pre- and post-buckled lipid micro/nano-tubules. It is seen that by taking the nonlocal size effect into consideration, the influence of geometrical parameters of the lipid micro/nano-tubule on the nonlinear vibration characteristics within the both prebuckling and postbuckling domains decreases and the frequency-deflection curves are more close to each other. However, the strain gradient size dependency has an opposite effect and leads to increase the gap between the frequency-deflection curves of axially compressed lipid micro/nano-tubules with different geometrical parameters.
具有高表面积比的独特几何形状使脂质微/纳米管成为一种出色的自组装超分子结构，可用于各种生物应用，如可控释放系统和药物递送。在本研究中，全面探讨了轴向加载的脂质微/纳米管在屈曲前和屈曲后区域相关的尺寸依赖性非线性振动。为实现这一目的，在三阶剪切可变形梁模型的框架内，采用了同时包含两种完全不同尺寸依赖性特征的非局部应变梯度弹性理论。借助哈密顿原理，建立了包含非线性屈曲前变形和大屈曲后挠度的非经典运动控制微分方程。最后，采用伽辽金方法结合改进的摄动技术，得到了屈曲前和屈曲后脂质微/纳米管非局部应变梯度非线性频率的显式解析表达式。可以看出考虑非局部尺寸效应后，脂质微/纳米管几何参数对屈曲前和屈曲后区域非线性振动特性的影响减小，频率-挠度曲线彼此更接近。然而，应变梯度尺寸依赖性具有相反的效果，导致不同几何参数的轴向压缩脂质微/纳米管的频率-挠度曲线之间的差距增大。
