{"id":"W4303578971","doi":"10.3390/applmech3040070","title":"Undamped Free Vibration Analysis of Functionally Graded Beams: A Dynamic Finite Element Approach","year":2022,"lang":"en","type":"article","venue":"Applied Mechanics","topic":"Composite Structure Analysis and Optimization","field":"Engineering","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Finite element method; Vibration; Nonlinear system; Timoshenko beam theory; Mathematical analysis; Normal mode; Interpolation (computer graphics); Trigonometric functions; Structural engineering; Natural frequency; Beam (structure); Method of mean weighted residuals; Mathematics; Galerkin method; Engineering; Physics; Acoustics; Geometry; Classical mechanics","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":[0.0001551709,0.0001348311,0.0002701853,0.0004258627,0.0001221509,0.00001848344,0.0001965436,0.00004004657,0.000339438],"category_scores_gemma":[0.000004020636,0.0001499569,0.0001529927,0.001630071,0.000004478724,0.00003656751,0.00009546964,0.0001317102,9.81832e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001497119,"about_ca_system_score_gemma":0.0000162994,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007303959,"about_ca_topic_score_gemma":0.00003301687,"domain_scores_codex":[0.9989573,0.00001966871,0.0003254599,0.000206105,0.0003547365,0.0001367515],"domain_scores_gemma":[0.9994446,0.0000304361,0.00009735044,0.0003595607,0.00003521614,0.00003284974],"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":[0.00001510015,0.00003254486,0.000004167121,0.00001464491,0.0009650577,1.766673e-7,0.0001895589,0.9582669,0.01180352,0.02788751,0.00006094496,0.0007598453],"study_design_scores_gemma":[0.0002807174,0.00002580454,0.00008844683,5.979713e-7,0.00107303,3.538919e-7,0.0002448129,0.9937183,0.0006100578,0.003431459,0.0003831431,0.0001432711],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.008485282,0.00006551626,0.9898546,0.00001591791,0.00009821894,0.0001984835,0.0000721362,0.0001080913,0.001101711],"genre_scores_gemma":[0.9828451,0.00002289848,0.01518881,0.00005875898,0.00001551171,0.00009426004,0.001724965,0.00002327279,0.00002640552],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9746658,"threshold_uncertainty_score":0.6115066,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.004470962524785178,"score_gpt":0.1744352399603982,"score_spread":0.169964277435613,"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."}}