{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T18:32:27Z","timestamp":1762367547335,"version":"build-2065373602"},"reference-count":25,"publisher":"Public Library of Science (PLoS)","issue":"11","license":[{"start":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T00:00:00Z","timestamp":1762300800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100017533","name":"Ho Chi Minh City University of Technology and Education","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100017533","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>This study introduces an enhanced numerical approach for analyzing the dynamic behavior of a rotor-bearing system subjected to unbalanced excitation from a gearbox drive shaft. The Newmark-\u03b2 method with the integration of a variable time-step algorithm was used, allowing the system to be solved rapidly and accurately without compromising stability. This technique enables a precise computation of displacement and torsional deformation of the rotating shaft during its operational cycle. The proposed computational model is validated against experimental data, showing deviations of displacement in normal operation below the critical speed of about 6%. A comprehensive parametric analysis is conducted to evaluate the influence of rotational speed, trial mass, and initial phase angle on the system dynamics. The findings confirm that our enhanced numerical approach yields rapid convergence and reliable predictions, making it a valuable tool for dynamic analysis of rotating systems.<\/jats:p>","DOI":"10.1371\/journal.pone.0335632","type":"journal-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T18:29:49Z","timestamp":1762367389000},"page":"e0335632","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Investigation on the influence of unbalanced shaft component in gearbox on displacement using the Newmark-\u03b2 method"],"prefix":"10.1371","volume":"20","author":[{"given":"Thanh Lam","family":"Tran","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6852-1521","authenticated-orcid":true,"given":"Vinh Phoi","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chi Cuong","family":"Le","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1546-3174","authenticated-orcid":true,"given":"Thien Ngon","family":"Dang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,11,5]]},"reference":[{"key":"pone.0335632.ref001","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1115\/1.3169125","article-title":"Coupled torsional and transverse vibration of unbalanced rotor","volume":"52","author":"R Cohen","year":"1985","journal-title":"J Appl Mech"},{"issue":"2","key":"pone.0335632.ref002","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/S0022-460X(02)01240-3","article-title":"Coupled torsional\u2013lateral vibration analysis of geared shaft systems using mode synthesis","volume":"261","author":"M Ananda Rao","year":"2003","journal-title":"J Sound Vib"},{"key":"pone.0335632.ref003","article-title":"Transient characteristics of a dual-rotor system with intershaft bearing subjected to mass unbalance and base motions during start-up","author":"X Chen","year":"2018","journal-title":"ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition; 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