{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:42:41Z","timestamp":1740120161198,"version":"3.37.3"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","funder":[{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"crossref","award":["11532011"],"award-info":[{"award-number":["11532011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"crossref","award":["11702200"],"award-info":[{"award-number":["11702200"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2018,12,15]]},"abstract":"<jats:p> In this paper, the stationary response of a van der Pol vibro-impact system with Coulomb friction excited by Gaussian white noise is studied. The Zhuravlev nonsmooth transformation of the state variables is utilized to transform the original system to a new system without the impact term. Then, the stochastic averaging method is applied to the equivalent system to obtain the stationary probability density functions (pdfs). The accuracy of the analytical results obtained from the proposed procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different damping coefficients, restitution coefficients, amplitudes of friction and noise intensities on the response are discussed. Additionally, stochastic P-bifurcations are explored. <\/jats:p>","DOI":"10.1142\/s0218127418300434","type":"journal-article","created":{"date-parts":[[2018,12,12]],"date-time":"2018-12-12T03:06:44Z","timestamp":1544584004000},"page":"1830043","source":"Crossref","is-referenced-by-count":11,"title":["Response Analysis of van der Pol Vibro-Impact System with Coulomb Friction Under Gaussian White Noise"],"prefix":"10.1142","volume":"28","author":[{"given":"Meng","family":"Su","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Northwestern Polytechnical University, Xian 710072, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7822-0340","authenticated-orcid":false,"given":"Wei","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Northwestern Polytechnical University, Xian 710072, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guidong","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xidian University, Xi\u2019an 710071, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,12,12]]},"reference":[{"key":"S0218127418300434BIB001","first-page":"83","volume":"19","author":"Bai H.","year":"2000","journal-title":"J. Vibr. Shock"},{"key":"S0218127418300434BIB002","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1997.1389"},{"key":"S0218127418300434BIB003","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1995.0617"},{"key":"S0218127418300434BIB004","doi-asserted-by":"publisher","DOI":"10.1023\/B:NODY.0000045510.93602.ca"},{"key":"S0218127418300434BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7225(65)90045-5"},{"key":"S0218127418300434BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/S0997-7538(03)00015-9"},{"key":"S0218127418300434BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2007.07.070"},{"key":"S0218127418300434BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2008.08.013"},{"key":"S0218127418300434BIB009","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.45.600"},{"key":"S0218127418300434BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2014.02.006"},{"key":"S0218127418300434BIB011","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1994.1492"},{"key":"S0218127418300434BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.probengmech.2016.03.003"},{"key":"S0218127418300434BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-2697-1"},{"key":"S0218127418300434BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijmecsci.2016.12.009"},{"key":"S0218127418300434BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127414501296"},{"key":"S0218127418300434BIB016","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2002.806436"},{"key":"S0218127418300434BIB017","first-page":"879","volume":"28","author":"Qian Z.","year":"2015","journal-title":"J. Vibr. Engin."},{"key":"S0218127418300434BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/0022-460X(77)90557-0"},{"key":"S0218127418300434BIB019","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021963316988"},{"key":"S0218127418300434BIB020","doi-asserted-by":"publisher","DOI":"10.1088\/0964-1726\/23\/9\/095001"},{"key":"S0218127418300434BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(99)00016-0"},{"key":"S0218127418300434BIB022","first-page":"2997","volume":"47","author":"Wang X.","year":"2016","journal-title":"J. Central South Univ."},{"key":"S0218127418300434BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2013.09.008"},{"key":"S0218127418300434BIB024","doi-asserted-by":"publisher","DOI":"10.1115\/1.2890401"},{"key":"S0218127418300434BIB025","first-page":"130","volume":"27","author":"Zhang Y.","year":"2008","journal-title":"J. Vibr. Shock"},{"key":"S0218127418300434BIB026","first-page":"14","volume":"1","author":"Zhu W.","year":"1987","journal-title":"J. Vibr. Engin."},{"key":"S0218127418300434BIB027","first-page":"28","volume":"10","author":"Zhu W.","year":"1989","journal-title":"Acta Aeron. Astron. Sin."},{"key":"S0218127418300434BIB028","doi-asserted-by":"publisher","DOI":"10.1115\/1.3101980"},{"volume-title":"Stochastic Vibration","year":"1998","author":"Zhu W.","key":"S0218127418300434BIB029"},{"volume-title":"Nonlinear Stochastic Dynamics and Control: Framework of Hamiltonian Theory","year":"2003","author":"Zhu W.","key":"S0218127418300434BIB030"},{"key":"S0218127418300434BIB031","first-page":"1","volume":"4","author":"Zhu H.","year":"2015","journal-title":"Int. J. Dyn. Contr."},{"key":"S0218127418300434BIB032","first-page":"23","volume":"2","author":"Zhuravlev V. F.","year":"1976","journal-title":"Mech. Solids"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127418300434","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T15:57:22Z","timestamp":1565107042000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127418300434"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,12]]},"references-count":32,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2018,12,12]]},"published-print":{"date-parts":[[2018,12,15]]}},"alternative-id":["10.1142\/S0218127418300434"],"URL":"https:\/\/doi.org\/10.1142\/s0218127418300434","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2018,12,12]]}}}