{"id":"https://openalex.org/W2055755589","doi":"https://doi.org/10.1155/2014/414903","title":"Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance","display_name":"Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2055755589","doi":"https://doi.org/10.1155/2014/414903","mag":"2055755589"},"language":"en","primary_location":{"id":"doi:10.1155/2014/414903","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/414903","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/414903.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/414903.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100331490","display_name":"Dongmei Zhang","orcid":"https://orcid.org/0000-0002-6586-1114"},"institutions":[{"id":"https://openalex.org/I15823474","display_name":"Linyi University","ror":"https://ror.org/01knv0402","country_code":"CN","type":"education","lineage":["https://openalex.org/I15823474"]},{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dongmei Zhang","raw_affiliation_strings":["Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","School of Science, Linyi University, Shandong 276005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"School of Science, Linyi University, Shandong 276005, China","institution_ids":["https://openalex.org/I15823474"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101871193","display_name":"Fangqi Chen","orcid":"https://orcid.org/0000-0001-7104-0948"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fangqi Chen","raw_affiliation_strings":["Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100331490"],"corresponding_institution_ids":["https://openalex.org/I15823474","https://openalex.org/I9842412"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.13539311,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11870","display_name":"Structural Analysis and Optimization","score":0.9955999851226807,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.8005439043045044},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7172776460647583},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6846954822540283},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5665403604507446},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5051708817481995},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.48761096596717834},{"id":"https://openalex.org/keywords/resonance","display_name":"Resonance (particle physics)","score":0.4851032495498657},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.464438259601593},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.46349310874938965},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.45000341534614563},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.44049888849258423},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.43810567259788513},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4336523413658142},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.4159155488014221},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24225130677223206},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2345845103263855},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10450449585914612}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.8005439043045044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7172776460647583},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6846954822540283},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5665403604507446},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5051708817481995},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.48761096596717834},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.4851032495498657},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.464438259601593},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.46349310874938965},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.45000341534614563},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.44049888849258423},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.43810567259788513},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4336523413658142},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.4159155488014221},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24225130677223206},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2345845103263855},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10450449585914612},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/414903","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/414903","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/414903.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1425305795","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1425305795","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:414903","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/414903.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:56b443c0598346559b57765891323279","is_oa":true,"landing_page_url":"https://doaj.org/article/56b443c0598346559b57765891323279","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/414903","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/414903","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/414903.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.47999998927116394,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1307941504","display_name":null,"funder_award_id":"20133218110025","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G3098948493","display_name":"\u9ad8\u8d85\u97f3\u901f\u4e58\u6ce2\u98de\u884c\u5668\u82e5\u5e72\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u95ee\u9898\u7684\u7814\u7a76","funder_award_id":"11172125","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3657835467","display_name":null,"funder_award_id":"20133218110025","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2055755589.pdf","grobid_xml":"https://content.openalex.org/works/W2055755589.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W18581655","https://openalex.org/W21755201","https://openalex.org/W412086436","https://openalex.org/W1976416284","https://openalex.org/W1982516032","https://openalex.org/W2011790374","https://openalex.org/W2012220364","https://openalex.org/W2023460070","https://openalex.org/W2027229150","https://openalex.org/W2040332110","https://openalex.org/W2057003218","https://openalex.org/W2059134197","https://openalex.org/W2079315709","https://openalex.org/W2084847378","https://openalex.org/W2087604959","https://openalex.org/W2095258853","https://openalex.org/W2169003520","https://openalex.org/W2261719497"],"related_works":["https://openalex.org/W2393929457","https://openalex.org/W2353805507","https://openalex.org/W2012700469","https://openalex.org/W2392834684","https://openalex.org/W1978174352","https://openalex.org/W2740153008","https://openalex.org/W2342467592","https://openalex.org/W132867293","https://openalex.org/W4379507489","https://openalex.org/W2090584918"],"abstract_inverted_index":{"Stability":[0],"and":[1,19,30,44,65,69,73,91,110,116,124,145],"bifurcation":[2,94,109,119,143],"behaviors":[3,120],"for":[4,141],"a":[5,62,70,74],"model":[6],"of":[7,26,28,50,76,86,100],"simply":[8],"supported":[9],"functionally":[10],"graded":[11],"materials":[12],"rectangular":[13],"plate":[14],"subjected":[15],"to":[16,107,136],"the":[17,83,87,92,101,138,150],"transversal":[18],"in-plane":[20],"excitations":[21],"are":[22,54,59,96,127],"studied":[23,55],"by":[24,61],"means":[25],"combination":[27],"analytical":[29,115],"numerical":[31,117,139,146],"methods.":[32],"The":[33],"resonant":[34],"case":[35],"considered":[36],"here":[37],"is":[38,134],"1":[39,41],":":[40],"internal":[42],"resonances":[43],"primary":[45],"parametric":[46],"resonance.":[47],"Two":[48],"types":[49],"degenerated":[51],"equilibrium":[52,89],"points":[53],"in":[56,98],"detail,":[57],"which":[58,104],"characterized":[60],"double":[63,71],"zero":[64,72],"two":[66],"negative":[67],"eigenvalues,":[68],"pair":[75],"pure":[77],"imaginary":[78],"eigenvalues.":[79],"For":[80],"each":[81],"case,":[82],"stability":[84],"regions":[85],"initial":[88],"solution":[90],"critical":[93],"curves":[95],"obtained":[97],"terms":[99],"system":[102],"parameters":[103,123,126],"may":[105],"lead":[106],"Hopf":[108],"2D":[111],"torus.":[112],"With":[113],"both":[114],"methods,":[118],"on":[121],"damping":[122],"detuning":[125],"studied,":[128],"respectively.":[129],"A":[130],"time":[131],"integration":[132],"scheme":[133],"used":[135],"find":[137],"solutions":[140],"these":[142],"cases,":[144],"results":[147],"agree":[148],"with":[149],"analytic":[151],"predictions.":[152]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}
