{"id":"https://openalex.org/W2120461512","doi":"https://doi.org/10.1142/s021812741250006x","title":"NONLINEAR RESPONSE OF THE MASS-SPRING MODEL WITH NONSMOOTH STIFFNESS","display_name":"NONLINEAR RESPONSE OF THE MASS-SPRING MODEL WITH NONSMOOTH STIFFNESS","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2120461512","doi":"https://doi.org/10.1142/s021812741250006x","mag":"2120461512"},"language":"en","primary_location":{"id":"doi:10.1142/s021812741250006x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741250006x","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063752443","display_name":"Grzegorz Litak","orcid":"https://orcid.org/0000-0002-9647-8345"},"institutions":[{"id":"https://openalex.org/I122534668","display_name":"Marche Polytechnic University","ror":"https://ror.org/00x69rs40","country_code":"IT","type":"education","lineage":["https://openalex.org/I122534668"]},{"id":"https://openalex.org/I8264552","display_name":"Lublin University of Technology","ror":"https://ror.org/024zjzd49","country_code":"PL","type":"education","lineage":["https://openalex.org/I8264552"]}],"countries":["IT","PL"],"is_corresponding":true,"raw_author_name":"GRZEGORZ LITAK","raw_affiliation_strings":["Department of Applied Mechanics, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland","Dipartimento di Architettura, Costruzioni e Strutture, Universita Politecnica delle Marche, Via Brecce Bianche 60131 Ancona, Italy","Dipartimento di Architettura, Costruzioni e Strutture, Universita Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mechanics, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin, Poland","institution_ids":["https://openalex.org/I8264552"]},{"raw_affiliation_string":"Dipartimento di Architettura, Costruzioni e Strutture, Universita Politecnica delle Marche, Via Brecce Bianche 60131 Ancona, Italy","institution_ids":["https://openalex.org/I122534668"]},{"raw_affiliation_string":"Dipartimento di Architettura, Costruzioni e Strutture, Universita Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy","institution_ids":["https://openalex.org/I122534668"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083836332","display_name":"Jes\u00fas M. Seoane","orcid":"https://orcid.org/0000-0002-2723-6764"},"institutions":[{"id":"https://openalex.org/I182083151","display_name":"Universidad Rey Juan Carlos","ror":"https://ror.org/01v5cv687","country_code":"ES","type":"education","lineage":["https://openalex.org/I182083151"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"JES\u00daS M. SEOANE","raw_affiliation_strings":["Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain","institution_ids":["https://openalex.org/I182083151"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073695290","display_name":"Samuel Zambrano","orcid":"https://orcid.org/0000-0002-9384-2017"},"institutions":[{"id":"https://openalex.org/I182083151","display_name":"Universidad Rey Juan Carlos","ror":"https://ror.org/01v5cv687","country_code":"ES","type":"education","lineage":["https://openalex.org/I182083151"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"SAMUEL ZAMBRANO","raw_affiliation_strings":["Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain","institution_ids":["https://openalex.org/I182083151"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055264305","display_name":"Miguel A. F. Sanju\u00e1n","orcid":"https://orcid.org/0000-0003-3515-0837"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]},{"id":"https://openalex.org/I182083151","display_name":"Universidad Rey Juan Carlos","ror":"https://ror.org/01v5cv687","country_code":"ES","type":"education","lineage":["https://openalex.org/I182083151"]}],"countries":["CN","ES"],"is_corresponding":false,"raw_author_name":"MIGUEL A. F. SANJU\u00c1N","raw_affiliation_strings":["Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China","Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China","institution_ids":["https://openalex.org/I21193070"]},{"raw_affiliation_string":"Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s/n, 28933 M\u00f3stoles, Madrid, Spain","institution_ids":["https://openalex.org/I182083151"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063752443"],"corresponding_institution_ids":["https://openalex.org/I122534668","https://openalex.org/I8264552"],"apc_list":null,"apc_paid":null,"fwci":1.6978,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.84556533,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","issue":"01","first_page":"1250006","last_page":"1250006"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9829000234603882,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.876899242401123},{"id":"https://openalex.org/keywords/spring","display_name":"Spring (device)","score":0.7816218137741089},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7617820501327515},{"id":"https://openalex.org/keywords/restoring-force","display_name":"Restoring force","score":0.6555261611938477},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6405602693557739},{"id":"https://openalex.org/keywords/stiffness","display_name":"Stiffness","score":0.6330602765083313},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.5614949464797974},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5506948828697205},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5085304975509644},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.47046101093292236},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.4403479993343353},{"id":"https://openalex.org/keywords/spring-system","display_name":"Spring system","score":0.43185046315193176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4030282199382782},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.3568950295448303},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.35430651903152466},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3516964912414551},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26482099294662476},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.17271843552589417},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.08442267775535583}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.876899242401123},{"id":"https://openalex.org/C2778712887","wikidata":"https://www.wikidata.org/wiki/Q102836","display_name":"Spring (device)","level":2,"score":0.7816218137741089},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7617820501327515},{"id":"https://openalex.org/C175853643","wikidata":"https://www.wikidata.org/wiki/Q1185557","display_name":"Restoring force","level":2,"score":0.6555261611938477},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6405602693557739},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.6330602765083313},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.5614949464797974},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5506948828697205},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5085304975509644},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.47046101093292236},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4403479993343353},{"id":"https://openalex.org/C143131809","wikidata":"https://www.wikidata.org/wiki/Q7580787","display_name":"Spring system","level":3,"score":0.43185046315193176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4030282199382782},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3568950295448303},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35430651903152466},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3516964912414551},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26482099294662476},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.17271843552589417},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.08442267775535583},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021812741250006x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741250006x","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6899999976158142,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W144703883","https://openalex.org/W1556804633","https://openalex.org/W1783671139","https://openalex.org/W2000206891","https://openalex.org/W2005298377","https://openalex.org/W2040825728","https://openalex.org/W2049813195","https://openalex.org/W2068003521","https://openalex.org/W2069613788","https://openalex.org/W2072549489","https://openalex.org/W2076476325","https://openalex.org/W2086061639","https://openalex.org/W2089876099","https://openalex.org/W2091962608","https://openalex.org/W2126266865","https://openalex.org/W2137101191","https://openalex.org/W2167808907","https://openalex.org/W2501870970","https://openalex.org/W2898916015","https://openalex.org/W3123094903","https://openalex.org/W4247823135","https://openalex.org/W4285719527","https://openalex.org/W4388249796"],"related_works":["https://openalex.org/W1995825062","https://openalex.org/W2132151838","https://openalex.org/W2063622393","https://openalex.org/W2376984092","https://openalex.org/W1979821120","https://openalex.org/W2383642220","https://openalex.org/W1974167203","https://openalex.org/W2226479411","https://openalex.org/W1502842043","https://openalex.org/W2120461512"],"abstract_inverted_index":{"In":[0],"this":[1,17],"paper,":[2],"we":[3,19,64],"study":[4,50],"the":[5,9,29,40,52,55,66,72,83,87,91,103,119],"nonlinear":[6,10,60],"response":[7],"of":[8,28,54,68,74,86,93,121],"mass-spring":[11],"model":[12],"with":[13,33],"nonsmooth":[14],"stiffness.":[15],"For":[16],"purpose,":[18],"take":[20],"as":[21],"prototype":[22],"model,":[23],"a":[24],"system":[25,41],"that":[26],"consists":[27],"double-well":[30],"smooth":[31],"potential":[32,61],"an":[34,78],"additional":[35],"spring":[36,89],"component":[37],"acting":[38],"on":[39,51,116],"only":[42],"for":[43,58,62],"large":[44],"enough":[45],"displacement.":[46],"We":[47,109],"focus":[48],"our":[49,94,111],"analysis":[53,105],"homoclinic":[56],"orbits":[57],"such":[59],"which":[63],"observe":[65],"appearance":[67],"chaotic":[69],"motion":[70],"in":[71,90],"presence":[73],"damping":[75],"effects":[76],"and":[77,106],"external":[79],"harmonic":[80],"force,":[81],"analyzing":[82],"crucial":[84],"role":[85],"linear":[88],"dynamics":[92],"system.":[95],"The":[96],"results":[97],"are":[98],"shown":[99],"by":[100],"using":[101],"both":[102],"Melnikov":[104],"numerical":[107],"simulations.":[108],"expect":[110],"work":[112],"to":[113],"have":[114],"implications":[115],"problems":[117],"concerning":[118],"suspension":[120],"vehicles,":[122],"among":[123],"others.":[124]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}