{"id":"https://openalex.org/W2010588905","doi":"https://doi.org/10.1115/1.3644035","title":"Shock Spectra of a Nonlinear System","display_name":"Shock Spectra of a Nonlinear System","publication_year":1960,"publication_date":"1960-09-01","ids":{"openalex":"https://openalex.org/W2010588905","doi":"https://doi.org/10.1115/1.3644035","mag":"2010588905"},"language":"en","primary_location":{"id":"doi:10.1115/1.3644035","doi":"https://doi.org/10.1115/1.3644035","is_oa":false,"landing_page_url":"https://doi.org/10.1115/1.3644035","pdf_url":null,"source":{"id":"https://openalex.org/S124014869","display_name":"Journal of Applied Mechanics","issn_l":"0021-8936","issn":["0021-8936","1345-9139","1528-9036","1884-832X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310316053","host_organization_name":"ASM International","host_organization_lineage":["https://openalex.org/P4310316053"],"host_organization_lineage_names":["ASM International"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied 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/A5081201440","display_name":"William T. Thomson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"W. T. Thomson","raw_affiliation_strings":["Department of Engineering, University of California, Los Angeles, Calif"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering, University of California, Los Angeles, Calif","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081201440"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":5.1492,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.9403307,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"27","issue":"3","first_page":"528","last_page":"534"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9599999785423279,"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"}},"topics":[{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9599999785423279,"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/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.012500000186264515,"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/T10160","display_name":"Seismic Performance and Analysis","score":0.008899999782443047,"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/shock-spectra","display_name":"shock spectra","score":0.9900000095367432},{"id":"https://openalex.org/keywords/nonlinear-springs","display_name":"nonlinear springs","score":0.7540000081062317},{"id":"https://openalex.org/keywords/single-degree-of-freedom-system","display_name":"single-degree-of-freedom systems","score":0.9160000085830688},{"id":"https://openalex.org/keywords/pulsed-excitation","display_name":"pulsed excitation","score":0.859000027179718},{"id":"https://openalex.org/keywords/step-excitation","display_name":"step excitation","score":0.6790000200271606},{"id":"https://openalex.org/keywords/damping","display_name":"damping","score":0.7730000019073486},{"id":"https://openalex.org/keywords/rectangular-pulses","display_name":"rectangular pulses","score":0.6510000228881836},{"id":"https://openalex.org/keywords/arbitrary-pulse-shape","display_name":"arbitrary pulse shape","score":0.8270000219345093},{"id":"https://openalex.org/keywords/phase-plane-analysis","display_name":"phase plane analysis","score":0.7310000061988831},{"id":"https://openalex.org/keywords/peak-response","display_name":"peak response","score":0.824999988079071}],"concepts":[{"id":"https://openalex.org/C2780167933","wikidata":"https://www.wikidata.org/wiki/Q1550652","display_name":"Pulse (music)","level":3,"score":0.7819898128509521},{"id":"https://openalex.org/C2781300812","wikidata":"https://www.wikidata.org/wiki/Q178061","display_name":"Shock (circulatory)","level":2,"score":0.7017340660095215},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.6923946142196655},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.613433301448822},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5682541131973267},{"id":"https://openalex.org/C169150495","wikidata":"https://www.wikidata.org/wiki/Q7259675","display_name":"Pulse duration","level":3,"score":0.5410076975822449},{"id":"https://openalex.org/C83581075","wikidata":"https://www.wikidata.org/wiki/Q1361503","display_name":"Excitation","level":2,"score":0.5013086795806885},{"id":"https://openalex.org/C99762115","wikidata":"https://www.wikidata.org/wiki/Q7499878","display_name":"Shock response spectrum","level":3,"score":0.4806579351425171},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.37974289059638977},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.372883141040802},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36646243929862976},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.2492685616016388},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.22115382552146912},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12896651029586792},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.1068415641784668},{"id":"https://openalex.org/C520434653","wikidata":"https://www.wikidata.org/wiki/Q38867","display_name":"Laser","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1115/1.3644035","doi":"https://doi.org/10.1115/1.3644035","is_oa":false,"landing_page_url":"https://doi.org/10.1115/1.3644035","pdf_url":null,"source":{"id":"https://openalex.org/S124014869","display_name":"Journal of Applied Mechanics","issn_l":"0021-8936","issn":["0021-8936","1345-9139","1528-9036","1884-832X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310316053","host_organization_name":"ASM International","host_organization_lineage":["https://openalex.org/P4310316053"],"host_organization_lineage_names":["ASM International"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mechanics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, justice, and strong institutions","score":0.8299999833106995}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4281681099","https://openalex.org/W2369611126","https://openalex.org/W3108224219","https://openalex.org/W2096473248","https://openalex.org/W2371298155","https://openalex.org/W33672286","https://openalex.org/W2375585101","https://openalex.org/W2216021223","https://openalex.org/W3035855245","https://openalex.org/W2071884304"],"abstract_inverted_index":{"The":[0,83],"peak":[1,93],"response":[2],"under":[3],"pulse":[4,38,49,57,69,72],"excitation,":[5,39],"of":[6,70,103],"a":[7,52,59],"single-degree-of-freedom":[8],"system":[9],"with":[10,31,48,78],"nonlinear":[11],"spring":[12],"approximated":[13],"by":[14],"two":[15],"straight":[16],"lines,":[17],"is":[18,62],"analytically":[19],"determined.":[20],"Shock":[21],"spectra":[22,42,85],"for":[23,43,66],"the":[24,36,40,55,67,79,91,96,101],"step":[25],"and":[26,64],"delta":[27],"function":[28],"are":[29,46,81,87],"developed":[30],"damping":[32,45],"as":[33,51],"parameter.":[34,53],"For":[35,54],"rectangular":[37],"shock":[41,84],"zero":[44],"presented":[47,86],"duration":[50],"arbitrary":[56],"shape,":[58],"general":[60],"procedure":[61],"discussed":[63],"illustrated":[65],"sine":[68],"differing":[71],"duration.":[73],"Generalized":[74],"phase-plane":[75],"plots":[76],"associated":[77],"problem":[80],"included.":[82],"applicable":[88],"only":[89],"when":[90],"first":[92],"corresponds":[94],"to":[95],"maximum":[97],"response,":[98],"thereby":[99],"avoiding":[100],"questions":[102],"unloading.":[104]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-10-08T09:06:37.294493","created_date":"2025-10-10T00:00:00"}