{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T10:08:16Z","timestamp":1785838096628,"version":"3.56.0"},"reference-count":38,"publisher":"AIP Publishing","issue":"2","funder":[{"name":"Hebei Provincial Central Guidance Local Science and Technology Development Funding Project","award":["246Z1913G"],"award-info":[{"award-number":["246Z1913G"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12272241"],"award-info":[{"award-number":["12272241"]}],"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":[[2025,2,1]]},"abstract":"<jats:p>The present work investigates stochastic P-bifurcation phenomena in a Duffing\u2013van der Pol vibro-impact oscillator containing a Bingham model under Gaussian white noise excitation. By employing non-smooth transformations and stochastic averaging techniques, an approximate analytical method is proposed to analyze the stochastic response and bifurcation behavior of nonlinear systems with friction and vibro-impact effects. Using a non-smooth transformation, the stochastically excited vibro-impact oscillator is converted into an approximately equivalent system without velocity discontinuities. Subsequently, the friction term is handled, and stochastic averaging is applied to derive the averaged stochastic It\u00f4 equation. The corresponding Fokker\u2013Planck\u2013Kolmogorov equation is then solved to obtain the probability density function of the system's steady-state response. Numerical simulations are conducted to verify the reliability of the proposed method. Based on these results, the critical parameter conditions for stochastic P-bifurcation are derived using singularity theory, considering both the amplitude probability density and the joint probability density of system displacement and velocity. Bifurcation diagrams, extreme value plots, amplitude probability density plots, velocity probability density plots, and joint probability density plots of system displacement and velocity are constructed for different parameter spaces. The findings demonstrate that changes in the viscous damping coefficient of the magnetorheological damper, Coulomb damping force, noise intensity, vibro-impact coefficient, and nonlinear damping coefficient can all induce stochastic P-bifurcations.<\/jats:p>","DOI":"10.1063\/5.0246296","type":"journal-article","created":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T21:00:18Z","timestamp":1738789218000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Random P-bifurcation in a Duffing\u2013van der Pol vibro-impact system with a Bingham model"],"prefix":"10.1063","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-5388-680X","authenticated-orcid":false,"given":"Zijian","family":"Kan","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Shijiazhuang Tiedao University 1 , Shijiazhuang 050043,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9017-5431","authenticated-orcid":false,"given":"Jun","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Shijiazhuang Tiedao University 1 , Shijiazhuang 050043,","place":["China"]},{"name":"State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University 2 , Shijiazhuang 050043,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-7163-3932","authenticated-orcid":false,"given":"Jianchao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Shijiazhuang Tiedao University 1 , Shijiazhuang 050043,","place":["China"]},{"name":"State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University 2 , Shijiazhuang 050043,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2154-8214","authenticated-orcid":false,"given":"Jiangchuan","family":"Niu","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Shijiazhuang Tiedao University 1 , Shijiazhuang 050043,","place":["China"]},{"name":"State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University 2 , Shijiazhuang 050043,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2025,2,5]]},"reference":[{"key":"2025020521001015100_c1","volume-title":"Nonlinear Stochastic Dynamics and Control","year":"2003"},{"key":"2025020521001015100_c2","volume-title":"Numerical Analysis Methods for Stochastic Dynamics System","year":"2013"},{"issue":"9","key":"2025020521001015100_c3","doi-asserted-by":"publisher","first-page":"163","DOI":"10.13465\/j.cnki.Jvs.2009.09.015","article-title":"Dynamic analysis of collision vibration system under random interference","volume":"28","year":"2009","journal-title":"J. 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