{"id":"W2079188570","doi":"10.1115/detc2004-57789","title":"Vibration Analysis of Axially Loaded Beams Including Rotary Inertia: An Exact Dynamic Finite Element","year":2004,"lang":"en","type":"article","venue":"","topic":"Vibration and Dynamic Analysis","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Axial symmetry; Rotary inertia; Finite element method; Cantilever; Vibration; Beam (structure); Virtual work; Timoshenko beam theory; Trigonometric functions; Inertia; Stiffness; Bending stiffness; Direct stiffness method; Bending; Structural engineering; Stiffness matrix; Mathematical analysis; Physics; Mechanics; Classical mechanics; Mathematics; Engineering; Acoustics; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001436651,0.0001588822,0.000318506,0.0006117639,0.00005800316,0.00003404542,0.0001292605,0.00007805171,0.000492321],"category_scores_gemma":[0.0000159668,0.000152468,0.0001792561,0.001296944,0.00001837192,0.0003802099,0.00002756462,0.00008551979,0.00001309623],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001480834,"about_ca_system_score_gemma":0.00002678476,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002032884,"about_ca_topic_score_gemma":0.001839089,"domain_scores_codex":[0.9988909,0.00002393299,0.0004806019,0.0001927437,0.000236858,0.0001749451],"domain_scores_gemma":[0.9994876,0.00002266849,0.00007176631,0.0002822969,0.00005234714,0.00008336701],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000005452764,0.00004360038,0.0005359776,0.00001201207,0.0008065855,0.000001456162,0.0003035665,0.978514,0.01809808,0.0004110087,0.000006151907,0.001262174],"study_design_scores_gemma":[0.0003147005,0.0000418439,0.006850589,0.000007079792,0.0005990756,2.888361e-7,0.0002075827,0.9872295,0.004397683,0.0001658971,0.00001358139,0.0001721343],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2410136,0.00002791739,0.7573478,0.00008729185,0.0000372009,0.00007837269,0.00001043635,0.0001745933,0.001222747],"genre_scores_gemma":[0.9914123,0.00003004167,0.007922743,0.000111611,0.00001764244,0.000009062212,0.0004173371,0.00001890045,0.00006032564],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7503987,"threshold_uncertainty_score":0.6217466,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01075810894891366,"score_gpt":0.2393326138227908,"score_spread":0.2285745048738771,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}