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Torsional wave and vibration subjected to constraint of surface elasticity

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A Correction to this article was published on 26 May 2018

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Abstract

Torsional waves and vibration of shafts are familiar phenomena in a micro/nano-electro-mechanical system (MEMS/NEMS). However, the characteristics of the torsional wave and vibration at nanoscale are different from their behaviors at macroscale due to the surface elasticity being disregarded at macroscale. In order to clarify these differences, we investigate the influence of surface elasticity on the torsional wave and vibration in a cylindrical rod. The results show that the surface elasticity weakens the dispersive effect of the torsional wave and causes a harmonic torsional wave without dispersion existing only when the surface wave velocity is equal to the bulk wave velocity. As the ratio of bulk to surface wave velocity is approaching 1, a jump will occur in the frequency of torsional vibration and the dispersion of the torsional wave. Finally, the theoretical framework of surface elasticity is extended into the Lagrangian field theory with interfacial dynamic constraint condition. The variational formulation of the Lagrangian field subjected to interfacial dynamic constraint is established.

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Change history

  • 26 May 2018

    The author regrets that the term in the integrand of the last row of Eq. (50) was omitted in the variational calculus of the paper cited above.

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing, 210016, People’s Republic of China

    Zaixing Huang

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  1. Zaixing Huang
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Correspondence to Zaixing Huang.

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Huang, Z. Torsional wave and vibration subjected to constraint of surface elasticity. Acta Mech 229, 1171–1182 (2018). https://doi.org/10.1007/s00707-017-2047-5

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  • DOI: https://doi.org/10.1007/s00707-017-2047-5

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