{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T21:46:20Z","timestamp":1785879980254,"version":"3.56.0"},"reference-count":33,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12372006"],"award-info":[{"award-number":["12372006"]}],"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":["12432001"],"award-info":[{"award-number":["12432001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.cnsns.2026.110439","type":"journal-article","created":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T00:03:57Z","timestamp":1781827437000},"page":"110439","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P3","title":["Nonlinear behavior of the first three symmetrical modes of a cable under harmonic excitation"],"prefix":"10.1016","volume":"162","author":[{"given":"Yang","family":"Long","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Houjun","family":"Kang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Quan","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoyang","family":"Su","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yueyu","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cnsns.2026.110439_bib0001","series-title":"Cable vibration in cable-stayed bridges","author":"Caetano","year":"2012"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110439_bib0002","first-page":"53","article-title":"Wind-rain induced vibration and its control on stay cables of cable-stayed bridges","volume":"36","author":"Wang","year":"2003","journal-title":"China Civ Eng J"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110439_bib0003","doi-asserted-by":"crossref","first-page":"1712","DOI":"10.1016\/j.jsv.2012.11.012","article-title":"Nonlinear in-plane vibrations of inclined cables carrying moving oscillators","volume":"332","author":"Sofi","year":"2013","journal-title":"J Sound Vib"},{"key":"10.1016\/j.cnsns.2026.110439_bib0004","unstructured":"Chen, S.S. (2002). Vibration, passive and semi-active control of cables for large-span cable-stayed bridges [Doctoral dissertation, Zhejiang University]. (in Chinese)."},{"issue":"1","key":"10.1016\/j.cnsns.2026.110439_bib0005","first-page":"52","article-title":"Property of nonlinear parametric vibration of CFRP cables","volume":"20","author":"Mei","year":"2007","journal-title":"China J Highw Transp"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110439_bib0006","first-page":"278","article-title":"Internal resonance analysis because of in-plane and out-of-plane coupling effects of the stay cable in the cable-stayed bridge II","volume":"25","author":"Xiao","year":"2008","journal-title":"Chin J Comput Mech"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110439_bib0007","first-page":"238","article-title":"Vector form intrinsic finite element (VFIFE) based simulation on vibration control of stay cables","volume":"27","author":"Ni","year":"2014","journal-title":"J Vib Eng"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110439_bib0008","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1115\/1.1777225","article-title":"Nonlinear vibrations of suspended cables\u2014Part II: deter ministic phenomena","volume":"57","author":"Rega","year":"2004","journal-title":"Appl Mech Rev"},{"key":"10.1016\/j.cnsns.2026.110439_bib0009","series-title":"Cable vibrations in cable-stayed bridges","author":"Caetano","year":"2011"},{"issue":"10","key":"10.1016\/j.cnsns.2026.110439_bib0010","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1016\/S0141-0296(99)00065-6","article-title":"Non-linear cable response to multiple support periodic excitation","volume":"22","author":"El-Attar","year":"2000","journal-title":"Eng Struct"},{"issue":"3\u20135","key":"10.1016\/j.cnsns.2026.110439_bib0011","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1016\/j.jsv.2004.01.022","article-title":"Nonlinear dynamics of cable stays. Part 1: sinusoidal cable support excitation","volume":"281","author":"Georgakis","year":"2005","journal-title":"J Sound Vib"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110439_bib0012","first-page":"144","article-title":"Analysis of in-plane parametric vibration of cables under axial excitation","volume":"15","author":"Chen","year":"2002","journal-title":"J Vib Eng"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110439_bib0013","first-page":"621","article-title":"Experimental and numerical studies of inclined cables: free and parametrically-forced vibrations","volume":"46","author":"Rega","year":"2008","journal-title":"J Theor Appl Mech"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110439_bib0014","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s00419-013-0792-z","article-title":"Nonlinear responses of a cable-beam coupled system under parametric and external excitations","volume":"84","author":"Wei","year":"2014","journal-title":"Arch Appl Mech"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110439_bib0015","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1006\/jsvi.1994.1261","article-title":"Vibration amplitudes caused by parametric excitation of cable-stayed structures","volume":"174","author":"Lilien","year":"1994","journal-title":"J Sound Vib"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110439_bib0016","first-page":"613","article-title":"Oscillations of bridge stay cables induced by periodic motions of deck and\/or towers","volume":"122","author":"Pinto da Costa","year":"1996","journal-title":"J Eng Mech"},{"key":"10.1016\/j.cnsns.2026.110439_bib0017","doi-asserted-by":"crossref","first-page":"4393","DOI":"10.1007\/s00707-018-2224-1","article-title":"Analytical solutions for planar simultaneous resonances of suspended cables involving two external periodic excitations","volume":"229","author":"Zhao","year":"2018","journal-title":"Acta Mech"},{"issue":"9","key":"10.1016\/j.cnsns.2026.110439_bib0018","doi-asserted-by":"crossref","DOI":"10.1142\/S0218127414300249","article-title":"Vibration dynamics of an inclined cable excited near its second natural frequency","volume":"24","author":"Tzanov","year":"2014","journal-title":"Int J Bifurc Chaos"},{"issue":"10","key":"10.1016\/j.cnsns.2026.110439_bib0019","article-title":"Analysis on in-plane 2:2:1 internal resonance of a complex cable-stayed bridge system under external harmonic excitation","volume":"16","author":"Kang","year":"2021","journal-title":"J Comput Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.110439_bib0020","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.jsv.2017.11.035","article-title":"Nonlinear vibration behaviors of suspended cables under two-frequency excitation with temperature effects","volume":"416","author":"Zhao","year":"2018","journal-title":"J Sound Vib"},{"key":"10.1016\/j.cnsns.2026.110439_bib0021","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2022.106988","article-title":"Vibration suppression of a cable under harmonic excitation by a nonlinear energy sink","volume":"117","author":"Wang","year":"2023","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110439_bib0022","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1006\/jsvi.1995.0232","article-title":"Nonlinear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions","volume":"182","author":"Benedettini","year":"1995","journal-title":"J Sound Vib"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110439_bib0023","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1006\/jsvi.1995.0553","article-title":"A nonlinear dynamic model for cables and its application to a cable structure system","volume":"187","author":"Warnitchai","year":"1995","journal-title":"J Sound Vib"},{"key":"10.1016\/j.cnsns.2026.110439_bib0024","doi-asserted-by":"crossref","first-page":"6023","DOI":"10.1016\/j.jsv.2011.07.027","article-title":"Bifurcation analysis of a parametrically excited inclined cable close to two-to-one internal resonance","volume":"330","author":"Marsico","year":"2011","journal-title":"J Sound Vib"},{"key":"10.1016\/j.cnsns.2026.110439_bib0025","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1007\/s11071-026-12421-y","article-title":"Experimental study on higher-order superharmonic resonance of cables in a scaled cable-stayed bridge model","volume":"114","author":"Kang","year":"2026","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.110439_bib0026","series-title":"Cable structures","author":"Irvine","year":"1981"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110439_bib0027","first-page":"644","article-title":"Temperature effects on the resonance responses of stay cables under support excitation","author":"Zhao","year":"2017","journal-title":"Chin J Comput Mech"},{"issue":"16","key":"10.1016\/j.cnsns.2026.110439_bib0028","doi-asserted-by":"crossref","first-page":"5685","DOI":"10.1016\/j.jsv.2012.07.010","article-title":"Modeling and analysis of the in-plane vibration of a complex cable-stayed bridge","volume":"331","author":"Cao","year":"2012","journal-title":"J Sound Vib"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110439_bib0029","first-page":"2299","article-title":"Modeling and analysis of the in-plane multiple \"1:1\" internal resonances in a cable-pylon coupled structure","volume":"103","author":"Chen","year":"2021","journal-title":"Nonlinear Dyn"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110439_bib0030","doi-asserted-by":"crossref","first-page":"1961","DOI":"10.1061\/(ASCE)0733-9445(1993)119:6(1961)","article-title":"Estimation curve for modal damping in stay cables with viscous damper","volume":"119","author":"Pacheco","year":"1993","journal-title":"J Struct Eng"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110439_bib0031","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1115\/1.2756064","article-title":"Nonlinear hybrid-mode resonant forced oscillations of sagged inclined cables at avoidances","volume":"2","author":"Rega","year":"2007","journal-title":"J Comput Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.110439_bib0032","series-title":"Beyond perturbation: introduction to homotopy analysis method","author":"Liao","year":"2003"},{"key":"10.1016\/j.cnsns.2026.110439_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2023.107351","article-title":"Parametric resonance of multi-frequency excited MEMS based on homotopy analysis method","volume":"125","author":"Yuan","year":"2023","journal-title":"Commun Nonlinear Sci Numer Simul"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426007938?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426007938?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T21:03:04Z","timestamp":1785877384000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570426007938"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":33,"alternative-id":["S1007570426007938"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110439","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Nonlinear behavior of the first three symmetrical modes of a cable under harmonic excitation","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110439","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"110439"}}