{"title":"杜芬振荡器的振动统计","authors":"Michalakis C. Constantinou","doi":"10.1016/0261-7277(85)90041-5","DOIUrl":null,"url":null,"abstract":"<div><p>The stationary response of the Duffing oscillator excited by white noise is considered. Based on the associated Fokker-Planck equation, the joint moments, of all orders, of the displacement and velocity are obtained in closed-form, in terms of parabolic cylinder functions. An asymptotic expansion, valid for large values of a dimensionless parameter, is also presented. It is shown that all moments of the Duffing oscillator are bounded by the corresponding moments of the linear oscillator.</p></div>","PeriodicalId":100715,"journal":{"name":"International Journal of Soil Dynamics and Earthquake Engineering","volume":"4 4","pages":"Pages 221-223"},"PeriodicalIF":0.0000,"publicationDate":"1985-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0261-7277(85)90041-5","citationCount":"2","resultStr":"{\"title\":\"Vibration statistics of the Duffing oscillator\",\"authors\":\"Michalakis C. Constantinou\",\"doi\":\"10.1016/0261-7277(85)90041-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The stationary response of the Duffing oscillator excited by white noise is considered. Based on the associated Fokker-Planck equation, the joint moments, of all orders, of the displacement and velocity are obtained in closed-form, in terms of parabolic cylinder functions. An asymptotic expansion, valid for large values of a dimensionless parameter, is also presented. It is shown that all moments of the Duffing oscillator are bounded by the corresponding moments of the linear oscillator.</p></div>\",\"PeriodicalId\":100715,\"journal\":{\"name\":\"International Journal of Soil Dynamics and Earthquake Engineering\",\"volume\":\"4 4\",\"pages\":\"Pages 221-223\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1985-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0261-7277(85)90041-5\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Soil Dynamics and Earthquake Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0261727785900415\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Soil Dynamics and Earthquake Engineering","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0261727785900415","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The stationary response of the Duffing oscillator excited by white noise is considered. Based on the associated Fokker-Planck equation, the joint moments, of all orders, of the displacement and velocity are obtained in closed-form, in terms of parabolic cylinder functions. An asymptotic expansion, valid for large values of a dimensionless parameter, is also presented. It is shown that all moments of the Duffing oscillator are bounded by the corresponding moments of the linear oscillator.
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