{"title":"Nonlinear Eigen frequencies of a functionally graded porous nano-beam with respect to the coulomb and Casimir forces","authors":"I. Papkova, T. Yakovleva","doi":"10.1051/e3sconf/202338901029","DOIUrl":null,"url":null,"abstract":"A new mathematical model of a porous functionally graded micro/nano-beam under the action of the Casimir force and the Coulomb force is constructed in this paper. The construction of the mathematical model takes into account the Euler-Bernoulli kinematic model. The dimensional-dependent parameter is taken into account by modified moment theory of elasticity. The variational, differential equations, boundary and initial conditions are derived from Ostrogradsky-Hamiltonian variational principle. The problem of non-linear natural oscillations of a beam under the action of force Casimir and Coulomb force is solved. The influence of the Casimir and Coulomb forces on the nonlinear eigenfrequencies of the micro/nano-beam is shown.","PeriodicalId":11445,"journal":{"name":"E3S Web of Conferences","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"E3S Web of Conferences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/e3sconf/202338901029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
A new mathematical model of a porous functionally graded micro/nano-beam under the action of the Casimir force and the Coulomb force is constructed in this paper. The construction of the mathematical model takes into account the Euler-Bernoulli kinematic model. The dimensional-dependent parameter is taken into account by modified moment theory of elasticity. The variational, differential equations, boundary and initial conditions are derived from Ostrogradsky-Hamiltonian variational principle. The problem of non-linear natural oscillations of a beam under the action of force Casimir and Coulomb force is solved. The influence of the Casimir and Coulomb forces on the nonlinear eigenfrequencies of the micro/nano-beam is shown.
期刊介绍：
E3S Web of Conferences is an Open Access publication series dedicated to archiving conference proceedings in all areas related to Environment, Energy and Earth Sciences. The journal covers the technological and scientific aspects as well as social and economic matters. Major disciplines include: soil sciences, hydrology, oceanography, climatology, geology, geography, energy engineering (production, distribution and storage), renewable energy, sustainable development, natural resources management… E3S Web of Conferences offers a wide range of services from the organization of the submission of conference proceedings to the worldwide dissemination of the conference papers. It provides an efficient archiving solution, ensuring maximum exposure and wide indexing of scientific conference proceedings. Proceedings are published under the scientific responsibility of the conference editors.
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