{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T10:17:10Z","timestamp":1790936230389,"version":"4.1.0"},"reference-count":52,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,4]],"date-time":"2020-02-04T00:00:00Z","timestamp":1580774400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The article presents mathematical considerations on the dynamics of the springing switch point being an element of the railway junction. Due to the structure of the switch point, mathematical analysis was divided into two stages: The first stage refers to the analysis of the dynamics of the switch point as a beam of variable rectilinear stiffness to which three forces (coming from three closures of switch drives) placed in the initial section of the switch point are applied. The next stage of the analysis concerns an identical beam, but curved, with a variable cross-section. In both cases, the beam is subjected to a vertical force resulting from forces from the rail vehicle. The calculations refer to a switch point of 23 m length and a curvature radius R = 1200 m. The first stage of the switch point analysis refers to the movement of a rail vehicle on a straight track, and the second stage concerns the rail vehicle movement on a reverse path. This article also provides an analysis of mode vibrations of a curved beam with a variable cross-section, and variable inertia and stiffness moments (further in the article the changes will be referred to as beam parameter changes). It is assumed that the beam is loaded with vertical forces (coming) from a rail vehicle. The solution was found by applying the Ritz method, which served to present the fourth-order partial equations as ordinary differential ones. The numerical research whose results are given aimed to define how the changes in beam parameters and vertical load affect mode vibrations of the beam.<\/jats:p>","DOI":"10.3390\/ma13030701","type":"journal-article","created":{"date-parts":[[2020,2,5]],"date-time":"2020-02-05T03:18:48Z","timestamp":1580872728000},"page":"701","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Numerical Testing of Switch Point Dynamics\u2014A Curved Beam with a Variable Cross-Section"],"prefix":"10.3390","volume":"13","author":[{"given":"Jerzy","family":"Kisilowski","sequence":"first","affiliation":[{"name":"Faculty of Transport, Electrical Engineering and Computer Science, University of Technology and Humanities, ul. Malczewskiego 29, 26-600 Radom, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6431-9561","authenticated-orcid":false,"given":"Rafa\u0142","family":"Kowalik","sequence":"additional","affiliation":[{"name":"Department of Avionics and Control Systems, Polish Air Force University, ul. Dywizjonu 303 nr 35, 08-521 Deblin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,4]]},"reference":[{"key":"ref_1","unstructured":"Akour, S. (July, January 30). Dynamics of nonlinear beam on elastic foundation. Proceedings of the World Congress on Engineering, London, UK."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1590\/S1679-78252011000200002","article-title":"Non-linear vibration of Euler-Bernoulli beams","volume":"8","author":"Barari","year":"2011","journal-title":"Lat. Ameri Can J. 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