{"title":"Variational principles for a double Rayleigh beam system undergoing vibrations and connected by a nonlinear Winkler–Pasternak elastic layer","authors":"S. Adali","doi":"10.1515/nleng-2022-0259","DOIUrl":null,"url":null,"abstract":"Abstract Variational principles and variationally consistent boundary conditions are derived for a system of double Rayleigh beams undergoing vibrations and subject to axial loads. The elastic layer connecting the beams are modelled as a three-parameter nonlinear Winkler–Pasternak layer with the Winkler layer having linear and nonlinear components and Pasternak layer having only a linear component. Variational principles are derived for the forced and freely vibrating double beam system using a semi-inverse approach. Hamilton’s principle for the system is given and the Rayleigh quotients are derived for the vibration frequency of the freely vibrating system and for the buckling load. Natural and geometric variationally consistent boundary conditions are derived which leads to a set of coupled boundary conditions due to the presence of Pasternak layer connecting the beams.","PeriodicalId":37863,"journal":{"name":"Nonlinear Engineering - Modeling and Application","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Engineering - Modeling and Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/nleng-2022-0259","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract Variational principles and variationally consistent boundary conditions are derived for a system of double Rayleigh beams undergoing vibrations and subject to axial loads. The elastic layer connecting the beams are modelled as a three-parameter nonlinear Winkler–Pasternak layer with the Winkler layer having linear and nonlinear components and Pasternak layer having only a linear component. Variational principles are derived for the forced and freely vibrating double beam system using a semi-inverse approach. Hamilton’s principle for the system is given and the Rayleigh quotients are derived for the vibration frequency of the freely vibrating system and for the buckling load. Natural and geometric variationally consistent boundary conditions are derived which leads to a set of coupled boundary conditions due to the presence of Pasternak layer connecting the beams.
期刊介绍:
The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.