This paper studies weak solutions of the axial oscillations of the carbon nanotube modeled as an elastic nanobeam surrounded by an elastic medium. The model used combines Eringen’s theory of non-local elasticity and the equations of axial oscillations proposed by Aydogdu. Based on the Sturm–Liouville problem associated with this case, the weak solutions of the longitudinal waves in the carbon nanotube are determined.

中文翻译：

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碳纳米管中纵波的弱解

本文研究了碳纳米管的轴向振荡的弱解，该碳纳米管建模为被弹性介质包围的弹性纳米束。使用的模型结合了艾林根的非局部弹性理论和Aydogdu提出的轴向振动方程。基于与此案例相关的Sturm-Liouville问题，确定了碳纳米管中纵波的弱解。