{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T20:56:22Z","timestamp":1779915382180,"version":"3.53.1"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T00:00:00Z","timestamp":1658361600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Education and Science of the Republic of Kazakhstan","award":["AP09261135"],"award-info":[{"award-number":["AP09261135"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This work aims at studying the nonlinear dynamics of drill strings using the lumped-parameter method (LPM). The study is based on the good consistency of the results of the test problem where the model of the longitudinal vibrations of a horizontal drill string with a static compressive load at the left end is considered. In this paper, this method is applied to discretize linear and nonlinear models of the lateral vibrations of a vertical drill string under the effect of a supersonic gas flow. The obtained results are verified with the previously published data. The optimal number of the drill-string partitions is determined using the developed application, which allows us to estimate the accuracy of the loaded data. The numerical solution of the model is obtained using the fourth-order Runge\u2013Kutta method. The optimization of the numerical algorithm using parallel-programming tools is carried out, and the efficiency of the method is analyzed.<\/jats:p>","DOI":"10.3390\/sym14071495","type":"journal-article","created":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T22:38:50Z","timestamp":1658443130000},"page":"1495","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Analysis of Drill-String Nonlinear Dynamics Using the Lumped-Parameter Method"],"prefix":"10.3390","volume":"14","author":[{"given":"Lelya A.","family":"Khajiyeva","sequence":"first","affiliation":[{"name":"Department of Mathematical and Computer Modelling, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Igor V.","family":"Andrianov","sequence":"additional","affiliation":[{"name":"Chair and Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstra\u00dfe 18, D-52062 Aachen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3497-0940","authenticated-orcid":false,"given":"Yuliya F.","family":"Sabirova","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computer Modelling, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9154-9653","authenticated-orcid":false,"given":"Askar K.","family":"Kudaibergenov","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computer Modelling, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,21]]},"reference":[{"key":"ref_1","unstructured":"International Association of Drilling Contractors (2000). 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