{"paper":{"title":"The Method of Strained Coordinates for Vibrations with Weak Unilateral Springs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"math.DS","authors_text":"Bernard Rousselet (JAD), St\\'ephane Junca (JAD)","submitted_at":"2009-06-15T15:11:30Z","abstract_excerpt":"We study some spring mass models for a structure having a unilateral spring of small rigidity $\\epsilon$. We obtain and justify an asymptotic expansion with the method of strained coordinates with new tools to handle such defects, including a non negligible cumulative effect over a long time: $T_\\eps \\sim \\eps^{-1}$ as usual; or, for a new critical case, we can only expect: $T_\\eps \\sim \\eps^{-1/2}$. We check numerically these results and present a purely numerical algorithm to compute \"Non linear Normal Modes\" (NNM); this algorithm provides results close to the asymptotic expansions but enabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2714","kind":"arxiv","version":2},"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"}