Vibration of a liquid-filled capillary tube

Shaobao Liu; Yufei Wu; Fan Yang; Moxiao Li; Xing Kou; Changsheng Lei; Feng Xu; Tian Jian Lu

doi:10.1016/j.jmbbm.2020.103745

Vibration of a liquid-filled capillary tube

J Mech Behav Biomed Mater. 2020 Jun:106:103745. doi: 10.1016/j.jmbbm.2020.103745. Epub 2020 Mar 26.

Authors

Shaobao Liu¹, Yufei Wu², Fan Yang³, Moxiao Li², Xing Kou⁴, Changsheng Lei⁴, Feng Xu⁵, Tian Jian Lu⁶

Affiliations

¹ State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, PR China; The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University, Shaanxi, 710049, PR China; Bioinspired Engineering & Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an, 710049, PR China.
² Bioinspired Engineering & Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an, 710049, PR China; State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, 710049, PR China.
³ State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, PR China.
⁴ State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, 710049, PR China.
⁵ The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi'an Jiaotong University, Shaanxi, 710049, PR China; Bioinspired Engineering & Biomechanics Center (BEBC), Xi'an Jiaotong University, Xi'an, 710049, PR China. Electronic address: fengxu@mail.xjtu.edu.cn.
⁶ State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, PR China; State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, 710049, PR China. Electronic address: tjlu@nuaa.edu.cn.

PMID: 32250955
DOI: 10.1016/j.jmbbm.2020.103745

Abstract

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.

Keywords: Beam-string structure; Interfacial tension; Mode transformation; Natural frequency; Size effect.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Capillary Tubing*
Vibration*