{"title":"具有中间弹性约束的双梁系统在运动力作用下的振动","authors":"F. Zakęś, P. Sniady","doi":"10.24423/ENGTRANS.1010.20190530","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate the problem of the dynamic behaviour of a double-beam system with intermediate elastic restraints subjected to a moving point force. Problem is solved by replacing this type of structure with two single-span beams loaded with a given moving force and redundant forces representing reactions in the intermediate restraints. Redundant forces are obtained by solving Volterra integral equations of the second order which are compatibility equations corresponding to each redundant. Solutions for the arbitrarily supported singlespan beam loaded with a moving point force and concentrated time-varying force are given. Difficulties in analytically solving Volterra integral equations are bypassed by applying a simple numerical procedure. Finally, a numerical example of a double-beam system with two elastic restraints is presented in order to show the effectiveness of the presented method.","PeriodicalId":38552,"journal":{"name":"Engineering Transactions","volume":"67 1","pages":"243-252"},"PeriodicalIF":0.0000,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Vibrations of a Double-Beam System with Intermediate Elastic Restraints Due to a Moving Force\",\"authors\":\"F. Zakęś, P. Sniady\",\"doi\":\"10.24423/ENGTRANS.1010.20190530\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we investigate the problem of the dynamic behaviour of a double-beam system with intermediate elastic restraints subjected to a moving point force. Problem is solved by replacing this type of structure with two single-span beams loaded with a given moving force and redundant forces representing reactions in the intermediate restraints. Redundant forces are obtained by solving Volterra integral equations of the second order which are compatibility equations corresponding to each redundant. Solutions for the arbitrarily supported singlespan beam loaded with a moving point force and concentrated time-varying force are given. Difficulties in analytically solving Volterra integral equations are bypassed by applying a simple numerical procedure. Finally, a numerical example of a double-beam system with two elastic restraints is presented in order to show the effectiveness of the presented method.\",\"PeriodicalId\":38552,\"journal\":{\"name\":\"Engineering Transactions\",\"volume\":\"67 1\",\"pages\":\"243-252\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-05-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Engineering Transactions\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24423/ENGTRANS.1010.20190530\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Transactions","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24423/ENGTRANS.1010.20190530","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Engineering","Score":null,"Total":0}
Vibrations of a Double-Beam System with Intermediate Elastic Restraints Due to a Moving Force
In this paper, we investigate the problem of the dynamic behaviour of a double-beam system with intermediate elastic restraints subjected to a moving point force. Problem is solved by replacing this type of structure with two single-span beams loaded with a given moving force and redundant forces representing reactions in the intermediate restraints. Redundant forces are obtained by solving Volterra integral equations of the second order which are compatibility equations corresponding to each redundant. Solutions for the arbitrarily supported singlespan beam loaded with a moving point force and concentrated time-varying force are given. Difficulties in analytically solving Volterra integral equations are bypassed by applying a simple numerical procedure. Finally, a numerical example of a double-beam system with two elastic restraints is presented in order to show the effectiveness of the presented method.
期刊介绍：
Engineering Transactions (formerly Rozprawy Inżynierskie) is a refereed international journal founded in 1952. The journal promotes research and practice in engineering science and provides a forum for interdisciplinary publications combining mechanics with: Material science, Mechatronics, Biomechanics and Biotechnologies, Environmental science, Photonics, Information technologies, Other engineering applications. The journal publishes original papers covering a broad area of research activities including: experimental and hybrid techniques, analytical and numerical approaches. Review articles and special issues are also welcome. Following long tradition, all articles are peer reviewed and our expert referees ensure that the papers accepted for publication comply with high scientific standards. Engineering Transactions is a quarterly journal intended to be interesting and useful for the researchers and practitioners in academic and industrial communities.
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