{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T13:21:26Z","timestamp":1775136086423,"version":"3.50.1"},"reference-count":39,"publisher":"AIP Publishing","issue":"9","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12402036"],"award-info":[{"award-number":["12402036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12262032"],"award-info":[{"award-number":["12262032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,9,1]]},"abstract":"<jats:p>Vibro-impact systems exhibit non-smooth characteristics and pose significant challenges for analysis. Non-smooth coordinate transformations are widely recognized for their ability to convert vibro-impact systems into systems with continuous trajectories, thereby enabling the application of some classical methods. This paper introduces an improved non-smooth coordinate transformation method [Su et al., Chaos 32, 043118 (2022)], developed from the Zhuravlev and Ivanov transformations, and extends it to the analysis of bilateral vibro-impact systems with stochastic excitations. We provide a detailed derivation of the transformation, which allows the conversion of the original non-smooth system into a form with continuous and periodic trajectories. According to two typical examples, the effectiveness of the proposed method is validated by solving the corresponding Fokker\u2013Planck equation and comparing the stationary probability density functions obtained from this approach with results from Monte\u2013Carlo simulations. The good agreement demonstrates that the improved transformation method, which can be directly applied to vibro-impact systems with asymmetric bilateral barriers accompanied with distinct restitution coefficients or a unilateral barrier, offers an effective tool for studying stochastic responses and bifurcations of such complex systems.<\/jats:p>","DOI":"10.1063\/5.0266439","type":"journal-article","created":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T13:03:52Z","timestamp":1757423032000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["An improved non-smooth coordinate transformation for analyzing bilateral vibro-impact systems with stochastic excitations"],"prefix":"10.1063","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4886-8960","authenticated-orcid":false,"given":"Meng","family":"Su","sequence":"first","affiliation":[{"name":"School of Mathematics, Northwest University 1 , Xi\u2019an 710127,","place":["People\u2019s Republic of China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-9952-9443","authenticated-orcid":false,"given":"Wenting","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Northwestern Polytechnical University 2 , Xi\u2019an 710129,","place":["People\u2019s Republic of China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4167-4885","authenticated-orcid":false,"given":"Li","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Ningxia University 3 , Yinchuan 750021,","place":["People\u2019s Republic of China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9802-8076","authenticated-orcid":false,"given":"Wei","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Northwestern Polytechnical University 2 , Xi\u2019an 710129,","place":["People\u2019s Republic of China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2025,9,9]]},"reference":[{"key":"2025090909034560100_c1","volume-title":"Vibro-Impact Dynamics: Modeling, Mapping and Applications","year":"2009"},{"key":"2025090909034560100_c2","volume-title":"Vibro-Impact Dynamics","year":"2012"},{"key":"2025090909034560100_c3","doi-asserted-by":"publisher","first-page":"5900","DOI":"10.1016\/j.jsv.2014.02.006","article-title":"Recent advances in vibro-impact dynamics and collision of ocean vessels","volume":"333","year":"2014","journal-title":"J. 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