Competing surface and geometric effects in the size-dependent vibrational response of hollow silicon nanobeams
- 1Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106, Warsaw, Poland
- 2Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Abstract
Classical continuum theories neglect surface-dominated effects that govern the mechanical response of nanostructures at high surface-to-volume ratios (SVR). Using molecular dynamics simulations, this work examines the size-dependent free transverse vibration of solid and hollow silicon nanobeams and shows that hollow geometries exhibit a non-monotonic dependence of natural frequency on cavity size, in contrast to the monotonic surface-induced softening displayed by solid nanobeams. For small cavities, geometric stiffening from the redistribution of material away from the neutral axis outweighs surface softening, increasing the frequency despite a rising SVR; as the cavity enlarges and the walls thin, the negative surface elastic constants of silicon dominate, producing a pronounced frequency drop. This competition is shown to be quantitatively consistent with an extension of the Miller–Shenoy surface-elasticity framework to hollow cross-sections, and is distilled into a minimal two-term dimensionless scaling law that balances a geometric stiffening term against a surface-softening term governed by the ratio of an intrinsic material length scale to the beam's outer dimension. The scaling law predicts the cavity ratio at which the stiffening-to-softening transition occurs, and the molecular dynamics results show this transition at a smaller cavity ratio than the continuum prediction, pointing to an additional, cross-section-dependent atomistic contribution to surface softening not captured by the linear continuum model. These results clarify the competing mechanisms governing the vibrational response of hollow nanobeams and provide a predictive, extensible framework connecting molecular-scale surface elasticity to continuum-level nanoscale design.
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BibTeX
@article{hassanpour2026competing,
title = {{Competing surface and geometric effects in the size-dependent vibrational response of hollow silicon nanobeams}},
author = {Akbar Hassanpour and Hamid M. Sedighi},
journal = {Multiscale and Multidisciplinary Modeling Experiments and Design},
year = {2026},
month = aug,
doi = {10.1007/s41939-026-01254-2},
url = {https://doi.org/10.1007/s41939-026-01254-2},
note = {CC BY},
}
RIS
TY - JOUR
TI - Competing surface and geometric effects in the size-dependent vibrational response of hollow silicon nanobeams
AU - Akbar Hassanpour
AU - Hamid M. Sedighi
PY - 2026
DA - 2026/08/05
JO - Multiscale and Multidisciplinary Modeling Experiments and Design
DO - 10.1007/s41939-026-01254-2
UR - https://doi.org/10.1007/s41939-026-01254-2
AB - Classical continuum theories neglect surface-dominated effects that govern the mechanical response of nanostructures at high surface-to-volume ratios (SVR). Using molecular dynamics simulations, this work examines the size-dependent free transverse vibration of solid and hollow silicon nanobeams and shows that hollow geometries exhibit a non-monotonic dependence of natural frequency on cavity size, in contrast to the monotonic surface-induced softening displayed by solid nanobeams. For small cavities, geometric stiffening from the redistribution of material away from the neutral axis outweighs surface softening, increasing the frequency despite a rising SVR; as the cavity enlarges and the walls thin, the negative surface elastic constants of silicon dominate, producing a pronounced frequency drop. This competition is shown to be quantitatively consistent with an extension of the Miller–Shenoy surface-elasticity framework to hollow cross-sections, and is distilled into a minimal two-term dimensionless scaling law that balances a geometric stiffening term against a surface-softening term governed by the ratio of an intrinsic material length scale to the beam's outer dimension. The scaling law predicts the cavity ratio at which the stiffening-to-softening transition occurs, and the molecular dynamics results show this transition at a smaller cavity ratio than the continuum prediction, pointing to an additional, cross-section-dependent atomistic contribution to surface softening not captured by the linear continuum model. These results clarify the competing mechanisms governing the vibrational response of hollow nanobeams and provide a predictive, extensible framework connecting molecular-scale surface elasticity to continuum-level nanoscale design.
SN - 2520-8160
SN - 2520-8179
ER -