{"title":"考虑到零初始条件下分子间作用力影响的功能分级静电驱动微梁的非线性振动","authors":"Dang Van Hieu","doi":"10.1007/s11029-024-10211-4","DOIUrl":null,"url":null,"abstract":"<p>Within the framework of the nonlocal strain gradient and the Euler–Bernoulli beam theories, a model of electrostatically actuated functionally graded (FG) microbeams is developed taking into account the intermolecular interaction forces in it. In addition to the electrostatic forces resulting from the applied DC voltage between a fixed substrate and the FG microbeam, the Casimir and van der Waals forces were also considered. The governing equation of motion of FG microbeams was derived by employing the Hamilton principle. Utilizing the Galerkin and the equivalent linearization methods, an analytical solution was obtained for the nonlinear vibration problem with zero initial conditions. To validate the accuracy of the results obtained, our solution was compared with the numerical and analytic solutions published in the literature.</p>","PeriodicalId":18308,"journal":{"name":"Mechanics of Composite Materials","volume":"33 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonlinear Vibration of Functionally Graded Electrostatically Actuated Microbeams Considering the Influence of Intermolecular Forces with Zero Initial Conditions\",\"authors\":\"Dang Van Hieu\",\"doi\":\"10.1007/s11029-024-10211-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Within the framework of the nonlocal strain gradient and the Euler–Bernoulli beam theories, a model of electrostatically actuated functionally graded (FG) microbeams is developed taking into account the intermolecular interaction forces in it. In addition to the electrostatic forces resulting from the applied DC voltage between a fixed substrate and the FG microbeam, the Casimir and van der Waals forces were also considered. The governing equation of motion of FG microbeams was derived by employing the Hamilton principle. Utilizing the Galerkin and the equivalent linearization methods, an analytical solution was obtained for the nonlinear vibration problem with zero initial conditions. To validate the accuracy of the results obtained, our solution was compared with the numerical and analytic solutions published in the literature.</p>\",\"PeriodicalId\":18308,\"journal\":{\"name\":\"Mechanics of Composite Materials\",\"volume\":\"33 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mechanics of Composite Materials\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://doi.org/10.1007/s11029-024-10211-4\",\"RegionNum\":4,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATERIALS SCIENCE, COMPOSITES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Composite Materials","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1007/s11029-024-10211-4","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATERIALS SCIENCE, COMPOSITES","Score":null,"Total":0}
Nonlinear Vibration of Functionally Graded Electrostatically Actuated Microbeams Considering the Influence of Intermolecular Forces with Zero Initial Conditions
Within the framework of the nonlocal strain gradient and the Euler–Bernoulli beam theories, a model of electrostatically actuated functionally graded (FG) microbeams is developed taking into account the intermolecular interaction forces in it. In addition to the electrostatic forces resulting from the applied DC voltage between a fixed substrate and the FG microbeam, the Casimir and van der Waals forces were also considered. The governing equation of motion of FG microbeams was derived by employing the Hamilton principle. Utilizing the Galerkin and the equivalent linearization methods, an analytical solution was obtained for the nonlinear vibration problem with zero initial conditions. To validate the accuracy of the results obtained, our solution was compared with the numerical and analytic solutions published in the literature.
期刊介绍:
Mechanics of Composite Materials is a peer-reviewed international journal that encourages publication of original experimental and theoretical research on the mechanical properties of composite materials and their constituents including, but not limited to:
damage, failure, fatigue, and long-term strength;
methods of optimum design of materials and structures;
prediction of long-term properties and aging problems;
nondestructive testing;
mechanical aspects of technology;
mechanics of nanocomposites;
mechanics of biocomposites;
composites in aerospace and wind-power engineering;
composites in civil engineering and infrastructure
and other composites applications.