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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