{
  "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.",
  "abstract_shown": true,
  "affiliations": [
    "Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106, Warsaw, Poland",
    "Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Akbar Hassanpour",
      "orcid": "0009-0009-0159-3067"
    },
    {
      "affs": [
        1
      ],
      "name": "Hamid M. Sedighi",
      "orcid": "0000-0002-3852-5473"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6emskz48s3cye.bib",
  "cited_by": 5,
  "doi": "10.1007/s41939-026-01254-2",
  "fulltext_url": null,
  "id": "6emskz48s3cye",
  "issns": [
    "2520-8160",
    "2520-8179"
  ],
  "landing_url": "https://doi.org/10.1007/s41939-026-01254-2",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2505|Nonlocal and gradient elasticity in micro/nano structures"
    ]
  ],
  "openalex": "W7172499155",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s41939-026-01254-2.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-05",
  "publisher": "Springer Science+Business Media",
  "ris": "https://research.draconitic.com/paper/6emskz48s3cye.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T13:21:14Z",
      "native_id": "W7172499155",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s41939-026-01254-2"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "openalex:2505|Nonlocal and gradient elasticity in micro/nano structures",
      "subfield": "materials-polymers"
    }
  ],
  "title": "Competing surface and geometric effects in the size-dependent vibrational response of hollow silicon nanobeams",
  "title_text": "Competing surface and geometric effects in the size-dependent vibrational response of hollow silicon nanobeams",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T13:20:45Z",
  "url": "https://research.draconitic.com/paper/6emskz48s3cye",
  "venue": "Multiscale and Multidisciplinary Modeling Experiments and Design",
  "versions": []
}