{"title":"双向功能分级碳纳米管增强复合梁的自由振动分析","authors":"M. Pang, S. M. Zhou, B. L. Hu, Y. Q. Zhang","doi":"10.1134/S0021894423050176","DOIUrl":null,"url":null,"abstract":"<p>Based on the Timoshenko beam theory, the vibration properties of a bidirectional functionally graded carbon nanotube reinforced composite beam are investigated. The governing equation of free vibration for the composite beam is derived, which considers the main influential factors, such as the gradient index and the distribution, aspect ratio, and volume ratio of carbon nanotubes. The differential quadrature method is used to solve the governing equation. The natural frequency of the composite beam is obtained. It is found that the natural frequency and vibration mode shapes of the beam are dependent upon the gradient index, nanotube distribution, and volume ratio of nanotubes. However, it should be pointed out that the nanotube distribution in the height direction and the volume ratio of nanotubes have very limited effects on the mode shapes of the composite beam.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":"64 5","pages":"878 - 889"},"PeriodicalIF":0.5000,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"FREE VIBRATION ANALYSIS OF A BIDIRECTIONAL FUNCTIONALLY GRADED CARBON NANOTUBE REINFORCED COMPOSITE BEAM\",\"authors\":\"M. Pang, S. M. Zhou, B. L. Hu, Y. Q. Zhang\",\"doi\":\"10.1134/S0021894423050176\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Based on the Timoshenko beam theory, the vibration properties of a bidirectional functionally graded carbon nanotube reinforced composite beam are investigated. The governing equation of free vibration for the composite beam is derived, which considers the main influential factors, such as the gradient index and the distribution, aspect ratio, and volume ratio of carbon nanotubes. The differential quadrature method is used to solve the governing equation. The natural frequency of the composite beam is obtained. It is found that the natural frequency and vibration mode shapes of the beam are dependent upon the gradient index, nanotube distribution, and volume ratio of nanotubes. However, it should be pointed out that the nanotube distribution in the height direction and the volume ratio of nanotubes have very limited effects on the mode shapes of the composite beam.</p>\",\"PeriodicalId\":608,\"journal\":{\"name\":\"Journal of Applied Mechanics and Technical Physics\",\"volume\":\"64 5\",\"pages\":\"878 - 889\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-01-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mechanics and Technical Physics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0021894423050176\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics and Technical Physics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0021894423050176","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
FREE VIBRATION ANALYSIS OF A BIDIRECTIONAL FUNCTIONALLY GRADED CARBON NANOTUBE REINFORCED COMPOSITE BEAM
Based on the Timoshenko beam theory, the vibration properties of a bidirectional functionally graded carbon nanotube reinforced composite beam are investigated. The governing equation of free vibration for the composite beam is derived, which considers the main influential factors, such as the gradient index and the distribution, aspect ratio, and volume ratio of carbon nanotubes. The differential quadrature method is used to solve the governing equation. The natural frequency of the composite beam is obtained. It is found that the natural frequency and vibration mode shapes of the beam are dependent upon the gradient index, nanotube distribution, and volume ratio of nanotubes. However, it should be pointed out that the nanotube distribution in the height direction and the volume ratio of nanotubes have very limited effects on the mode shapes of the composite beam.
期刊介绍：
Journal of Applied Mechanics and Technical Physics is a journal published in collaboration with the Siberian Branch of the Russian Academy of Sciences. The Journal presents papers on fluid mechanics and applied physics. Each issue contains valuable contributions on hypersonic flows; boundary layer theory; turbulence and hydrodynamic stability; free boundary flows; plasma physics; shock waves; explosives and detonation processes; combustion theory; multiphase flows; heat and mass transfer; composite materials and thermal properties of new materials, plasticity, creep, and failure.
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