{"id":"https://openalex.org/W7168291320","doi":"https://doi.org/10.1098/rspa.2026.0255","title":"Asymmetric hill equations arising from bilinear oscillators with state-dependent parametric excitation","display_name":"Asymmetric hill equations arising from bilinear oscillators with state-dependent parametric excitation","publication_year":2026,"publication_date":"2026-11-04","ids":{"openalex":"https://openalex.org/W7168291320","doi":"https://doi.org/10.1098/rspa.2026.0255"},"language":"en","primary_location":{"id":"doi:10.1098/rspa.2026.0255","doi":"https://doi.org/10.1098/rspa.2026.0255","is_oa":true,"landing_page_url":"https://doi.org/10.1098/rspa.2026.0255","pdf_url":"https://royalsocietypublishing.org/rspa/article-pdf/doi/10.1098/rspa.2026.0255/6174967/rspa.2026.0255.pdf","source":{"id":"https://openalex.org/S3006183880","display_name":"Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences","issn_l":"1364-5021","issn":["1364-5021","1471-2946"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319787","host_organization_name":"Royal Society","host_organization_lineage":["https://openalex.org/P4310319787"],"host_organization_lineage_names":["Royal Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Royal Society A Mathematical Physical and Engineering Science","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://royalsocietypublishing.org/rspa/article-pdf/doi/10.1098/rspa.2026.0255/6174967/rspa.2026.0255.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140593153","display_name":"Anish Kumar","orcid":"https://orcid.org/0000-0002-2370-8437","observed_orcids":["https://orcid.org/0000-0002-2370-8437"]},"institutions":[{"id":"https://openalex.org/I882761360","display_name":"Indian Institute of Space Science and Technology","ror":"https://ror.org/05k37ht14","country_code":"IN","type":"education","lineage":["https://openalex.org/I882761360"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Anish Kumar","raw_affiliation_strings":["Department of Aerospace Engineering, Indian Institute of Space Science and Technology , Thiruvananthapuram, India"],"raw_orcid":"https://orcid.org/0000-0002-2370-8437","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, Indian Institute of Space Science and Technology , Thiruvananthapuram, India","institution_ids":["https://openalex.org/I882761360"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5140593153"],"corresponding_institution_ids":["https://openalex.org/I882761360"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.38857885,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"482","issue":"2349","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T12435","display_name":"Bladed Disk Vibration Dynamics","score":0.0044999998062849045,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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":0.002199999988079071,"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/bilinear-oscillator","display_name":"bilinear oscillator","score":0.9819999933242798},{"id":"https://openalex.org/keywords/transition-curves","display_name":"transition curves","score":0.7879999876022339},{"id":"https://openalex.org/keywords/primary-resonance","display_name":"primary resonance","score":0.7179999947547913},{"id":"https://openalex.org/keywords/subharmonic-resonance","display_name":"subharmonic resonance","score":0.9919999837875366},{"id":"https://openalex.org/keywords/dynamic-instability","display_name":"dynamic instability","score":0.8259999752044678},{"id":"https://openalex.org/keywords/rotor-dynamics","display_name":"rotor dynamics","score":0.45100000500679016}],"concepts":[{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6432999968528748},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5519999861717224},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.532800018787384},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5184999704360962},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.508899986743927},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.48820000886917114},{"id":"https://openalex.org/C141354745","wikidata":"https://www.wikidata.org/wiki/Q17227","display_name":"Cantilever","level":2,"score":0.487199991941452},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.47940000891685486},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.4740999937057495},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.45579999685287476},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43939998745918274},{"id":"https://openalex.org/C40678858","wikidata":"https://www.wikidata.org/wiki/Q6934874","display_name":"Multiple-scale analysis","level":3,"score":0.41600000858306885},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4074999988079071},{"id":"https://openalex.org/C83581075","wikidata":"https://www.wikidata.org/wiki/Q1361503","display_name":"Excitation","level":2,"score":0.40540000796318054},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3937000036239624},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.38179999589920044},{"id":"https://openalex.org/C164466805","wikidata":"https://www.wikidata.org/wiki/Q2632607","display_name":"Parametric oscillator","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.34119999408721924},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.31119999289512634},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.30379998683929443},{"id":"https://openalex.org/C2777834885","wikidata":"https://www.wikidata.org/wiki/Q13417156","display_name":"Flutter","level":3,"score":0.30379998683929443},{"id":"https://openalex.org/C29373527","wikidata":"https://www.wikidata.org/wiki/Q753658","display_name":"Subharmonic function","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2953999936580658},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C171912257","wikidata":"https://www.wikidata.org/wiki/Q11019","display_name":"Mechanical system","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C117185709","wikidata":"https://www.wikidata.org/wiki/Q381448","display_name":"Aeroelasticity","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.25279998779296875}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1098/rspa.2026.0255","doi":"https://doi.org/10.1098/rspa.2026.0255","is_oa":true,"landing_page_url":"https://doi.org/10.1098/rspa.2026.0255","pdf_url":"https://royalsocietypublishing.org/rspa/article-pdf/doi/10.1098/rspa.2026.0255/6174967/rspa.2026.0255.pdf","source":{"id":"https://openalex.org/S3006183880","display_name":"Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences","issn_l":"1364-5021","issn":["1364-5021","1471-2946"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319787","host_organization_name":"Royal Society","host_organization_lineage":["https://openalex.org/P4310319787"],"host_organization_lineage_names":["Royal Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Royal Society A Mathematical Physical and Engineering Science","raw_type":"journal-article"},{"id":"doi:10.31224/7575","doi":"https://doi.org/10.31224/7575","is_oa":true,"landing_page_url":"https://doi.org/10.31224/7575","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.1098/rspa.2026.0255","doi":"https://doi.org/10.1098/rspa.2026.0255","is_oa":true,"landing_page_url":"https://doi.org/10.1098/rspa.2026.0255","pdf_url":"https://royalsocietypublishing.org/rspa/article-pdf/doi/10.1098/rspa.2026.0255/6174967/rspa.2026.0255.pdf","source":{"id":"https://openalex.org/S3006183880","display_name":"Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences","issn_l":"1364-5021","issn":["1364-5021","1471-2946"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319787","host_organization_name":"Royal Society","host_organization_lineage":["https://openalex.org/P4310319787"],"host_organization_lineage_names":["Royal Society"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Royal Society A Mathematical Physical and Engineering Science","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7168291320.pdf","grobid_xml":"https://content.openalex.org/works/W7168291320.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W274870236","https://openalex.org/W1964222293","https://openalex.org/W1965558582","https://openalex.org/W1981243560","https://openalex.org/W1997359704","https://openalex.org/W1999940485","https://openalex.org/W2004938259","https://openalex.org/W2008651591","https://openalex.org/W2012069094","https://openalex.org/W2012681042","https://openalex.org/W2018006978","https://openalex.org/W2021907377","https://openalex.org/W2030276379","https://openalex.org/W2036417529","https://openalex.org/W2046406985","https://openalex.org/W2059932998","https://openalex.org/W2077533207","https://openalex.org/W2090379665","https://openalex.org/W2099772914","https://openalex.org/W2104981807","https://openalex.org/W2161010981","https://openalex.org/W2605324095","https://openalex.org/W2924477257","https://openalex.org/W3081914953","https://openalex.org/W3196969473","https://openalex.org/W4280599808","https://openalex.org/W4293078920","https://openalex.org/W4312222570","https://openalex.org/W4365506297","https://openalex.org/W4404448083","https://openalex.org/W7125128704","https://openalex.org/W7165110143"],"related_works":["https://openalex.org/W2132384949","https://openalex.org/W4392006672","https://openalex.org/W2788307442","https://openalex.org/W4402724157","https://openalex.org/W4382280868","https://openalex.org/W1991140835","https://openalex.org/W4409214727","https://openalex.org/W814297361","https://openalex.org/W2063570691","https://openalex.org/W4236408330"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"study":[2],"presents":[3],"an":[4,119],"analytical":[5],"and":[6,22,55,76,83,108,113,137],"numerical":[7,59],"investigation":[8],"of":[9,41],"bilinear":[10],"oscillators":[11],"subjected":[12],"to":[13,45,90],"piecewise":[14,130],"parametric":[15,37],"excitation,":[16],"where":[17],"both":[18],"the":[19,47,64,101,104],"excitation":[20],"amplitude":[21],"damping":[23],"are":[24,29,67],"state-dependent.":[25],"The":[26,39,85,115],"governing":[27],"equations":[28,34],"formulated":[30],"as":[31,135],"asymmetric":[32,36,105],"Hill\u2019s":[33],"with":[35,97,110,139],"excitation.":[38,114],"method":[40],"averaging":[42],"is":[43,53,87],"employed":[44],"derive":[46],"corresponding":[48],"slow-flow":[49],"equations,":[50],"whose":[51],"stability":[52],"analysed":[54],"validated":[56],"against":[57],"direct":[58],"simulations.":[60],"Closed-form":[61],"expressions":[62],"for":[63,74,122],"transition":[65],"curves":[66],"developed,":[68],"providing":[69],"insight":[70],"into":[71],"instability":[72,125],"boundaries":[73],"primary":[75],"subharmonic":[77],"resonance":[78],"conditions":[79],"(1:1,":[80],"2:1,":[81],"3:1":[82],"4:1).":[84],"analysis":[86],"further":[88],"extended":[89],"a":[91,98],"physically":[92],"relevant":[93],"system\u2014a":[94],"cantilever":[95],"beam":[96],"breathing":[99,140],"crack\u2014demonstrating":[100],"equivalence":[102],"between":[103],"Hill":[106],"model":[107],"structures":[109],"state-dependent":[111,132],"stiffness":[112],"proposed":[116],"framework":[117],"establishes":[118],"efficient":[120],"approach":[121],"predicting":[123],"dynamic":[124],"in":[126],"engineering":[127],"systems":[128],"exhibiting":[129],"or":[131],"nonlinearities,":[133],"such":[134],"beams":[136],"rotors":[138],"cracks.":[141]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-07-15T00:00:00"}
