{
  "abstract": "Optimizing slender elastic structures for renewable energy applications requires non-classical continuum formulations capable of accounting for spatial micro-interactions without sacrificing analytical tractability. Here, we extend beam vibration mechanics by replacing standard spatial derivatives with the Dunkl differential operator. This modification introduces a reflection-coupled mathematical structure that accounts for spatial parity effects across the beam domain. We formulate the governing dynamic equations into a generalized eigenvalue problem and derive exact analytical expressions for modal characteristics under standard boundary conditions. The classical limit confirms exact convergence to classical Euler-Bernoulli formulations. Parametric analyses reveal that the Dunkl parameter acts as a reflection-induced modulation parameter, significantly shifting natural frequencies and altering the modal characteristics of higher modes. These results provide an analytical baseline for dynamic optimization in lightweight structural components.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09369",
  "author_total": 1,
  "authors": [
    {
      "name": "Hacene Bouguerne"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cfn2atrjyggg1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09369",
  "fulltext_url": null,
  "id": "cfn2atrjyggg1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09369",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.class-ph"
    ],
    [
      "openalex",
      "2505|Nonlocal and gradient elasticity in micro/nano structures"
    ]
  ],
  "openalex": "W7212121163",
  "pdf_url": "https://arxiv.org/pdf/2609.09369",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cfn2atrjyggg1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.09369",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09369"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "openalex:2505|Nonlocal and gradient elasticity in micro/nano structures",
      "subfield": "materials-polymers"
    }
  ],
  "title": "Dunkl-Based Modeling of Vibrational Modes in Lightweight Elastic Beams",
  "title_text": "Dunkl-Based Modeling of Vibrational Modes in Lightweight Elastic Beams",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/cfn2atrjyggg1",
  "venue": "arXiv",
  "versions": []
}