{"title":"对具有一般边界条件的嵌入式非局部 CNTRC 梁的自由振动进行精确高效的分析模拟","authors":"","doi":"10.1016/j.physb.2024.416556","DOIUrl":null,"url":null,"abstract":"<div><div>This study aims to evaluate the free vibrational response of embedded restrained nanobeams enriched by nanocomposites based on an exact Fourier series approach. In order to capture the small-scale effects on the dynamical response, Eringen's differential form of nonlocal elasticity is used which employs a scale (nonlocal) parameter. Within the framework of Rayleigh and Bernoulli-Euler beam theories, including the effect of nonlocality and employing the Fourier sine series together with Stokes' transformation, systems of linear equations are obtained and solved using the coefficient matrices. The combined effects of elastic boundary conditions, elastic foundation, dispersion patterns and volume fractions of carbon nanotubes, and nonlocal parameter are examined by solving eigenvalue problems constructed with Fourier infinite series. Free vibration frequencies are calculated for carbon nanotube-reinforced nanobeams under different rigid or restrained boundary conditions, including Winkler-Pasternak type elastic foundation. A comprehensive parametric study is performed, focusing on various effects for the free vibrational response of the composite nanobeam reinforced with carbon nanotubes. It is concluded that adding a small amount of carbon nanotube material can reinforce the stiffness of the composite nanobeam, and its free vibration performance is significantly affected by the distribution patterns, elastic medium, and boundary conditions.</div></div>","PeriodicalId":20116,"journal":{"name":"Physica B-condensed Matter","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Accurate and efficient analytical simulation of free vibration for embedded nonlocal CNTRC beams with general boundary conditions\",\"authors\":\"\",\"doi\":\"10.1016/j.physb.2024.416556\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This study aims to evaluate the free vibrational response of embedded restrained nanobeams enriched by nanocomposites based on an exact Fourier series approach. In order to capture the small-scale effects on the dynamical response, Eringen's differential form of nonlocal elasticity is used which employs a scale (nonlocal) parameter. Within the framework of Rayleigh and Bernoulli-Euler beam theories, including the effect of nonlocality and employing the Fourier sine series together with Stokes' transformation, systems of linear equations are obtained and solved using the coefficient matrices. The combined effects of elastic boundary conditions, elastic foundation, dispersion patterns and volume fractions of carbon nanotubes, and nonlocal parameter are examined by solving eigenvalue problems constructed with Fourier infinite series. Free vibration frequencies are calculated for carbon nanotube-reinforced nanobeams under different rigid or restrained boundary conditions, including Winkler-Pasternak type elastic foundation. A comprehensive parametric study is performed, focusing on various effects for the free vibrational response of the composite nanobeam reinforced with carbon nanotubes. It is concluded that adding a small amount of carbon nanotube material can reinforce the stiffness of the composite nanobeam, and its free vibration performance is significantly affected by the distribution patterns, elastic medium, and boundary conditions.</div></div>\",\"PeriodicalId\":20116,\"journal\":{\"name\":\"Physica B-condensed Matter\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physica B-condensed Matter\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0921452624008974\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, CONDENSED MATTER\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica B-condensed Matter","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0921452624008974","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, CONDENSED MATTER","Score":null,"Total":0}
Accurate and efficient analytical simulation of free vibration for embedded nonlocal CNTRC beams with general boundary conditions
This study aims to evaluate the free vibrational response of embedded restrained nanobeams enriched by nanocomposites based on an exact Fourier series approach. In order to capture the small-scale effects on the dynamical response, Eringen's differential form of nonlocal elasticity is used which employs a scale (nonlocal) parameter. Within the framework of Rayleigh and Bernoulli-Euler beam theories, including the effect of nonlocality and employing the Fourier sine series together with Stokes' transformation, systems of linear equations are obtained and solved using the coefficient matrices. The combined effects of elastic boundary conditions, elastic foundation, dispersion patterns and volume fractions of carbon nanotubes, and nonlocal parameter are examined by solving eigenvalue problems constructed with Fourier infinite series. Free vibration frequencies are calculated for carbon nanotube-reinforced nanobeams under different rigid or restrained boundary conditions, including Winkler-Pasternak type elastic foundation. A comprehensive parametric study is performed, focusing on various effects for the free vibrational response of the composite nanobeam reinforced with carbon nanotubes. It is concluded that adding a small amount of carbon nanotube material can reinforce the stiffness of the composite nanobeam, and its free vibration performance is significantly affected by the distribution patterns, elastic medium, and boundary conditions.
期刊介绍:
Physica B: Condensed Matter comprises all condensed matter and material physics that involve theoretical, computational and experimental work.
Papers should contain further developments and a proper discussion on the physics of experimental or theoretical results in one of the following areas:
-Magnetism
-Materials physics
-Nanostructures and nanomaterials
-Optics and optical materials
-Quantum materials
-Semiconductors
-Strongly correlated systems
-Superconductivity
-Surfaces and interfaces