{"id":"https://openalex.org/W1985449964","doi":"https://doi.org/10.1016/0266-8920(93)90017-p","title":"Approximate solution for nonlinear random vibration problems by partial stochastic linearization","display_name":"Approximate solution for nonlinear random vibration problems by partial stochastic linearization","publication_year":1993,"publication_date":"1993-01-01","ids":{"openalex":"https://openalex.org/W1985449964","doi":"https://doi.org/10.1016/0266-8920(93)90017-p","mag":"1985449964"},"language":"en","primary_location":{"id":"doi:10.1016/0266-8920(93)90017-p","doi":"https://doi.org/10.1016/0266-8920(93)90017-p","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0266-8920(93)90017-p","pdf_url":null,"source":{"id":"https://openalex.org/S189810516","display_name":"Probabilistic Engineering Mechanics","issn_l":"0266-8920","issn":["0266-8920","1878-4275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Probabilistic Engineering Mechanics","raw_type":"journal-article"},"volume":null,"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/A5008409828","display_name":"Isaac E. Elishakoff","orcid":"https://orcid.org/0000-0002-1723-7771","observed_orcids":["https://orcid.org/0000-0002-1723-7771"]},"institutions":[{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"I. Elishakoff","raw_affiliation_strings":["Center for Applied Stochastic Research and Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, Florida 33431-0991, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Stochastic Research and Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, Florida 33431-0991, USA","institution_ids":["https://openalex.org/I63772739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031485839","display_name":"Guoqiang Cai","orcid":"https://orcid.org/0000-0002-6804-9033","observed_orcids":["https://orcid.org/0000-0002-6804-9033"]},"institutions":[{"id":"https://openalex.org/I63772739","display_name":"Florida Atlantic University","ror":"https://ror.org/05p8w6387","country_code":"US","type":"education","lineage":["https://openalex.org/I63772739"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G.Q. Cai","raw_affiliation_strings":["Center for Applied Stochastic Research and Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, Florida 33431-0991, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Stochastic Research and Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, Florida 33431-0991, USA","institution_ids":["https://openalex.org/I63772739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I63772739"],"apc_list":{"value":3370,"currency":"USD","value_usd":3370},"apc_paid":null,"fwci":3.1841,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.89650092,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"8","issue":"3-4","first_page":"233","last_page":"237"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9214000105857849,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9214000105857849,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.06430000066757202,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.004699999932199717,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-random-vibration","display_name":"nonlinear random vibration","score":0.8629999756813049},{"id":"https://openalex.org/keywords/equivalent-linearization","display_name":"equivalent linearization","score":0.8830000162124634},{"id":"https://openalex.org/keywords/nonlinear-damping","display_name":"nonlinear damping","score":0.6890000104904175},{"id":"https://openalex.org/keywords/linear-viscous-damping","display_name":"linear viscous damping","score":0.8939999938011169},{"id":"https://openalex.org/keywords/equivalent-damping-coefficient","display_name":"equivalent damping coefficient","score":0.7450000047683716},{"id":"https://openalex.org/keywords/nonlinear-restoring-force","display_name":"nonlinear restoring force","score":0.781000018119812},{"id":"https://openalex.org/keywords/stochastic-differential-equations","display_name":"stochastic differential equations","score":0.7599999904632568},{"id":"https://openalex.org/keywords/approximate-solutions","display_name":"approximate solutions","score":0.5669999718666077}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.8290795087814331},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.7800151705741882},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6920046806335449},{"id":"https://openalex.org/C85736874","wikidata":"https://www.wikidata.org/wiki/Q672139","display_name":"Feedback linearization","level":3,"score":0.5533824563026428},{"id":"https://openalex.org/C130076159","wikidata":"https://www.wikidata.org/wiki/Q7291997","display_name":"Random vibration","level":3,"score":0.5239139795303345},{"id":"https://openalex.org/C175853643","wikidata":"https://www.wikidata.org/wiki/Q1185557","display_name":"Restoring force","level":2,"score":0.5045315027236938},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.47986310720443726},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4731767475605011},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46551015973091125},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4536735713481903},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44113969802856445},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.43661829829216003},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4172552525997162},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.1536594033241272},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14272162318229675},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1168762743473053},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0266-8920(93)90017-p","doi":"https://doi.org/10.1016/0266-8920(93)90017-p","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0266-8920(93)90017-p","pdf_url":null,"source":{"id":"https://openalex.org/S189810516","display_name":"Probabilistic Engineering Mechanics","issn_l":"0266-8920","issn":["0266-8920","1878-4275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Probabilistic Engineering Mechanics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W226487207","https://openalex.org/W1003308462","https://openalex.org/W1523936606","https://openalex.org/W1536233603","https://openalex.org/W1978080760","https://openalex.org/W1998455280","https://openalex.org/W2009405201","https://openalex.org/W2012548929","https://openalex.org/W2028697190","https://openalex.org/W2055343764","https://openalex.org/W2480173016","https://openalex.org/W4249214341","https://openalex.org/W6626285330","https://openalex.org/W6721849768"],"related_works":["https://openalex.org/W72847221","https://openalex.org/W2799288890","https://openalex.org/W2012548929","https://openalex.org/W1978994739","https://openalex.org/W1985702870","https://openalex.org/W88567187","https://openalex.org/W2029316251","https://openalex.org/W63032750","https://openalex.org/W2054675324","https://openalex.org/W2025671399"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2016-06-24T00:00:00"}