{"paper":{"title":"Free Vibrations of Axisymmetric Shells: Parabolic and Elliptic cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP","physics.class-ph"],"primary_cat":"math.NA","authors_text":"Erwan Faou (IRMAR, IPSO), Marie Chaussade-Beaudouin (IRMAR), Monique Dauge (IRMAR), Zohar Yosibash","submitted_at":"2016-02-02T09:39:03Z","abstract_excerpt":"Approximate eigenpairs (quasimodes) of axisymmetric thin elastic domains with laterally clamped boundary conditions (Lam{\\'e} system) are determined by an asymptotic analysis as the thickness ($2\\varepsilon$) tends to zero. The departing point is the Koiter shell model that we reduce by asymptotic analysis to a scalar modelthat depends on two parameters: the angular frequency $k$ and the half-thickness $\\varepsilon$. Optimizing $k$ for each chosen $\\varepsilon$, we find power laws for $k$ in function of $\\varepsilon$ that provide the smallest eigenvalues of the scalar reductions.Corresponding "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00850","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}