{"paper":{"title":"Frequency-Domain Analysis of the Euler-Bernoulli and Timoshenko Beams with Attached Masses","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Transfer functions are obtained for Timoshenko and Euler-Bernoulli beams with attached masses and local damping via variational principles.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexander Zuyev, Julia Kalosha","submitted_at":"2025-07-29T18:26:21Z","abstract_excerpt":"This work focuses on the frequency-domain modeling of a control system with a flexible beam and a rigid body. A simply supported beam is equipped with a spring-loaded control actuator and possesses local damping effect. Using Hamilton's variational principle, the equations of motion are derived in the state space form taking into account interface conditions involving lumped control and local damping. The transfer functions are obtained for the Timoshenko and Euler--Bernoulli beam models with the output measurements provided by a point sensor. Comparative Bode plots are presented for the two b"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Transfer functions are obtained for the Timoshenko and Euler-Bernoulli beam models with the output measurements provided by a point sensor, and comparative Bode plots are presented for different choices of output signals and damping coefficients.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The interface conditions involving the lumped control actuator and local damping can be incorporated directly into the variational formulation without additional modeling approximations beyond those already present in the Euler-Bernoulli and Timoshenko theories.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives state-space models and transfer functions for Euler-Bernoulli and Timoshenko beams with control actuator and damping, then compares Bode plots across output choices.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Transfer functions are obtained for Timoshenko and Euler-Bernoulli beams with attached masses and local damping via variational principles.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"71e346381a029b532f1b672148f7dab20aeea96476b3f8ae725d2b085bce3ed9"},"source":{"id":"2507.22147","kind":"arxiv","version":5},"verdict":{"id":"f7499976-eef7-4c70-b1cf-626246cd3af5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T02:08:20.133309Z","strongest_claim":"Transfer functions are obtained for the Timoshenko and Euler-Bernoulli beam models with the output measurements provided by a point sensor, and comparative Bode plots are presented for different choices of output signals and damping coefficients.","one_line_summary":"Derives state-space models and transfer functions for Euler-Bernoulli and Timoshenko beams with control actuator and damping, then compares Bode plots across output choices.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The interface conditions involving the lumped control actuator and local damping can be incorporated directly into the variational formulation without additional modeling approximations beyond those already present in the Euler-Bernoulli and Timoshenko theories.","pith_extraction_headline":"Transfer functions are obtained for Timoshenko and Euler-Bernoulli beams with attached masses and local damping via variational principles."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.22147/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"}