{"paper":{"title":"Inverse Problems of Identifying the Unknown Transverse Shear Force in the Euler-Bernoulli Beam with Kelvin-Voigt Damping","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"A. Hasanov, D. Anjuna, K. Sakthivel","submitted_at":"2023-01-19T07:42:41Z","abstract_excerpt":"In this paper, we study the inverse problems of determining the unknown transverse shear force $g(t)$ in a system governed by the damped Euler-Bernoulli equation $\\rho(x)u_{tt}+\\mu(x)u_t+ (r(x)u_{xx})_{xx}+ (\\kappa(x)u_{xxt})_{xx}=0, ~(x,t)\\in (0,\\ell)\\times(0,T],$ subject to the boundary conditions $u(0,t) =0$, $u_{x}(0,t)=0$, $\\left[r(x)u_{xx}+\\kappa(x)u_{xxt}\\right]_{x=\\ell} =0$, $-\\left[\\big(r(x)u_{xx}+\\kappa(x)u_{xxt}\\big)_{x}\\right]_{x=\\ell}=g(t)$, $t\\in [0,T]$, from the measured deflection $\\nu(t):=u(\\ell,t)$, $t \\in [0,T]$, and from the bending moment $\\omega(t):=-\\left( r(0)u_{xx}(0,t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.07931","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.07931/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}