Liquid-filled capillary tubes are common structures in nature and engineering fields, which often function via vibration. Although liquid-solid interfacial tension plays important roles in the vibration behavior of the liquid-filled capillary tube, it remains elusive how the interfacial tension influences the natural frequency of capillary tube vibration. To address this, we developed a theory of beam-string structure to analyze the influence of liquid-solid interfacial tension on the vibration of a liquid-filled capillary cantilever. We used glass capillary tubes as a demo and experimentally validated the theory, where the reduced liquid-solid interfacial tension in a capillary tube decreases the natural frequencies of small-order modes. We then performed theoretical analysis and found that the change of elastocapillarity number, slenderness ratio and inner/outer radius ratio of capillary tubes enables: in higher order modes, a nonmonotonic change of natural frequency due to mode transformation between a beam and string; for lower order modes, decrease in the natural frequency to zero (increase from zero) due to mode disappearance (appearance). The developed theory would provide guidelines for high-accuracy design of capillary sensors.

充满液体的毛细管是自然和工程领域中的常见结构，通常通过振动起作用。尽管液固界面张力在充满液体的毛细管的振动行为中起着重要作用，但是仍然难以确定界面张力如何影响毛细管振动的固有频率。为了解决这个问题，我们开发了一种束弦结构理论，以分析液固界面张力对充液毛细管悬臂梁振动的影响。我们使用玻璃毛细管作为演示，并通过实验验证了该理论，其中毛细管中减小的液固界面张力会降低小阶模态的固有频率。然后，我们进行了理论分析，发现弹性毛细管数的变化，毛细管的细长比和内/外半径比使得：在高阶模中​​，由于梁和弦之间的模转换，固有频率非单调变化；对于低阶模式，由于模式消失（外观）而使固有频率降低到零（从零增加）。发达的理论将为毛细管传感器的高精度设计提供指导。