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Axisymmetric vibration of a soft elastic rod with surface tension-induced residual stress

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Abstract

This paper studies the axisymmetric vibration of a soft elastic rod with surface tension based on the modified Gurtin–Murdoch model. In contrast to the original Gurtin–Murdoch model (GM model) in which surface tension is treated as a finite value while the residual stress in the bulk induced by it is however treated as an infinitesimal quantity, the present modified model supposes both to be finite values. In addition to the effects of surface tension-induced residual stress in the bulk, those of the surface inertia and bulk axial prestress are incorporated in the present model, and particularly the dispersion relations are derived analytically for the cases of incompressible rods. Comparative results are given for the present model, the original GM model, and the classical elasticity model without surface tension, which reveal that the surface tension-induced residual stress in the bulk would play a crucial role in predicting the frequency of vibration of the rod when the dimensionless parameter (σ0/μR) ≥ 0.3, where (μ, R, σ0) are the shear modulus, the radius, and surface tension of the rod.

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Acknowledgements

The authors acknowledge the supports from the National Natural Science Foundation of China (11872203), Joint Fund of Advanced Aerospace Manufacturing Technology Research (U1937601), National Natural Science Foundation of China for Creative Research Groups (No. 51921003), China Postdoctoral Science Foundation (2021M701705), and an Initiation Research Project Funded by Jinling Institute of Technology (040521400118).

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Guang Yang, Luqiao Qi, Ming Dai & Cun-Fa Gao

  2. School of Electrical and Mechanical Engineering, Jinling Institute of Technology, Nanjing, 211169, China

    Pengyu Pei

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  1. Guang Yang
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Correspondence to Pengyu Pei or Cun-Fa Gao.

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Yang, G., Qi, L., Dai, M. et al. Axisymmetric vibration of a soft elastic rod with surface tension-induced residual stress. Acta Mech 233, 2405–2413 (2022). https://doi.org/10.1007/s00707-022-03221-7

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