{"title":"单自由度系统的Lucas多项式解","authors":"Nurcan Baykuş Savaşaneril","doi":"10.52460/src.2023.002","DOIUrl":null,"url":null,"abstract":"Free vibration of a single degree of freedom system is a fundamental topic in mechanical vibrations. The present study introduces a novel and simple numerical method for the solution of this system in terms of Lucas polynomials in the matrix form. Particular and general solutions of the differential equation can be determined by this method. The method is illustrated by a numerical application and the results obtained are compared with those of the exact solution.","PeriodicalId":400190,"journal":{"name":"Scientific Research Communications","volume":"223 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lucas Polynomial Solution of the Single Degree of Freedom System\",\"authors\":\"Nurcan Baykuş Savaşaneril\",\"doi\":\"10.52460/src.2023.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Free vibration of a single degree of freedom system is a fundamental topic in mechanical vibrations. The present study introduces a novel and simple numerical method for the solution of this system in terms of Lucas polynomials in the matrix form. Particular and general solutions of the differential equation can be determined by this method. The method is illustrated by a numerical application and the results obtained are compared with those of the exact solution.\",\"PeriodicalId\":400190,\"journal\":{\"name\":\"Scientific Research Communications\",\"volume\":\"223 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Scientific Research Communications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52460/src.2023.002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scientific Research Communications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52460/src.2023.002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Lucas Polynomial Solution of the Single Degree of Freedom System
Free vibration of a single degree of freedom system is a fundamental topic in mechanical vibrations. The present study introduces a novel and simple numerical method for the solution of this system in terms of Lucas polynomials in the matrix form. Particular and general solutions of the differential equation can be determined by this method. The method is illustrated by a numerical application and the results obtained are compared with those of the exact solution.
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