{"title":"研究FGM纳米光束固有频率的参数均匀化模型","authors":"Abdelhak Berkia, Billel Rebai, Bilal Litouche, Soufiane Abbas, Khelifa Mansouri","doi":"10.3934/matersci.2023048","DOIUrl":null,"url":null,"abstract":"<abstract> <p>This research focuses on exploring the free vibration behavior of functionally graded (FG) nano-beams. To calculate the effective properties of the FG nano-beam, which varies solely in the thickness direction, the four homogenization schemes Mori-Tanaka, Tamura, Reuss and Voigt are employed. This study employs high-order shear deformation nano-beam theory and derives the governing equations of motion using nonlocal differential constitutive relations of Eringen. Hamilton's principle is utilized in conjunction with the refined three variables beam theory. The consideration of a length scale parameter accounts for small-scale effects. Analytical solutions are obtained for a simply supported FG nano-beam and compared with existing literature solutions. The research also investigates the influence of different homogenization schemes, the nonlocal parameter, beam aspect ratio and various material compositions on the dynamic response of the FG nano-beam.</p> </abstract>","PeriodicalId":7670,"journal":{"name":"AIMS Materials Science","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Investigating parametric homogenization models for natural frequency of FGM nano beams\",\"authors\":\"Abdelhak Berkia, Billel Rebai, Bilal Litouche, Soufiane Abbas, Khelifa Mansouri\",\"doi\":\"10.3934/matersci.2023048\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<abstract> <p>This research focuses on exploring the free vibration behavior of functionally graded (FG) nano-beams. To calculate the effective properties of the FG nano-beam, which varies solely in the thickness direction, the four homogenization schemes Mori-Tanaka, Tamura, Reuss and Voigt are employed. This study employs high-order shear deformation nano-beam theory and derives the governing equations of motion using nonlocal differential constitutive relations of Eringen. Hamilton's principle is utilized in conjunction with the refined three variables beam theory. The consideration of a length scale parameter accounts for small-scale effects. Analytical solutions are obtained for a simply supported FG nano-beam and compared with existing literature solutions. The research also investigates the influence of different homogenization schemes, the nonlocal parameter, beam aspect ratio and various material compositions on the dynamic response of the FG nano-beam.</p> </abstract>\",\"PeriodicalId\":7670,\"journal\":{\"name\":\"AIMS Materials Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"AIMS Materials Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/matersci.2023048\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"AIMS Materials Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/matersci.2023048","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
Investigating parametric homogenization models for natural frequency of FGM nano beams
This research focuses on exploring the free vibration behavior of functionally graded (FG) nano-beams. To calculate the effective properties of the FG nano-beam, which varies solely in the thickness direction, the four homogenization schemes Mori-Tanaka, Tamura, Reuss and Voigt are employed. This study employs high-order shear deformation nano-beam theory and derives the governing equations of motion using nonlocal differential constitutive relations of Eringen. Hamilton's principle is utilized in conjunction with the refined three variables beam theory. The consideration of a length scale parameter accounts for small-scale effects. Analytical solutions are obtained for a simply supported FG nano-beam and compared with existing literature solutions. The research also investigates the influence of different homogenization schemes, the nonlocal parameter, beam aspect ratio and various material compositions on the dynamic response of the FG nano-beam.
期刊介绍:
AIMS Materials Science welcomes, but not limited to, the papers from the following topics: · Biological materials · Ceramics · Composite materials · Magnetic materials · Medical implant materials · New properties of materials · Nanoscience and nanotechnology · Polymers · Thin films.