Nonlinear forced vibration of the FGM piezoelectric microbeam with flexoelectric effect
In this paper, based on the extended dielectric theory, Euler beams theory and von Karman’s geometric nonlinearity, a nonlinear FGM piezoelectric microbeam model is established with flexoelectric effect. The governing equations, initial conditions and boundary conditions are obtained by applying Ham...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824011839 |
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| author | Lichang Shan Guangchun Xiao Anqing Li Shasha Zhou Li Wang Weiguang Su Yonglong Liu Lei Yang Xiaoyue Song |
| author_facet | Lichang Shan Guangchun Xiao Anqing Li Shasha Zhou Li Wang Weiguang Su Yonglong Liu Lei Yang Xiaoyue Song |
| author_sort | Lichang Shan |
| collection | DOAJ |
| description | In this paper, based on the extended dielectric theory, Euler beams theory and von Karman’s geometric nonlinearity, a nonlinear FGM piezoelectric microbeam model is established with flexoelectric effect. The governing equations, initial conditions and boundary conditions are obtained by applying Hamilton’s principle and then solved by combining the differential quadrature method (DQM) and iteration method. The innovation of this paper is to construct a nonlinear forced vibration model of piezoelectric microbeams. The coupling response between the inverse flexoelectric effect and the inverse piezoelectric effect is investigated. Various effects are examined, including the functional gradient index m and transverse distributed load q affecting the distribution of electric potential. Results indicated that the functional gradient index m, beam thickness h, and span-length ratio L/h have a significant impact on the dimensionless deflection of the FGM microbeam. The influence of the flexoelectric effect on dimensionless deflection increases with the decrease of scale. In addition, transverse load q and the functional gradient index m also have a significant impact on the distribution of electric potential. This paper will provide useful theoretical guidance for the design of micro-sensors and micro-actuators. |
| format | Article |
| id | doaj-art-26cd34dfedff4d99b620af86a03a09bb |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-26cd34dfedff4d99b620af86a03a09bb2025-01-09T06:13:24ZengElsevierAlexandria Engineering Journal1110-01682025-01-01110386399Nonlinear forced vibration of the FGM piezoelectric microbeam with flexoelectric effectLichang Shan0Guangchun Xiao1Anqing Li2Shasha Zhou3Li Wang4Weiguang Su5Yonglong Liu6Lei Yang7Xiaoyue Song8School of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China; Shandong Institute of Mechanical Design and Research, Jinan 250031, PR ChinaSchool of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China; Shandong Institute of Mechanical Design and Research, Jinan 250031, PR ChinaSchool of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China; Shandong Institute of Mechanical Design and Research, Jinan 250031, PR China; Corresponding author at: School of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China.School of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China; Shandong Institute of Mechanical Design and Research, Jinan 250031, PR ChinaSchool of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China; Shandong Institute of Mechanical Design and Research, Jinan 250031, PR ChinaSchool of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China; Shandong Institute of Mechanical Design and Research, Jinan 250031, PR ChinaSchool of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China; Shandong Institute of Mechanical Design and Research, Jinan 250031, PR ChinaSchool of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China; Shandong Institute of Mechanical Design and Research, Jinan 250031, PR ChinaSchool of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China; Shandong Institute of Mechanical Design and Research, Jinan 250031, PR ChinaIn this paper, based on the extended dielectric theory, Euler beams theory and von Karman’s geometric nonlinearity, a nonlinear FGM piezoelectric microbeam model is established with flexoelectric effect. The governing equations, initial conditions and boundary conditions are obtained by applying Hamilton’s principle and then solved by combining the differential quadrature method (DQM) and iteration method. The innovation of this paper is to construct a nonlinear forced vibration model of piezoelectric microbeams. The coupling response between the inverse flexoelectric effect and the inverse piezoelectric effect is investigated. Various effects are examined, including the functional gradient index m and transverse distributed load q affecting the distribution of electric potential. Results indicated that the functional gradient index m, beam thickness h, and span-length ratio L/h have a significant impact on the dimensionless deflection of the FGM microbeam. The influence of the flexoelectric effect on dimensionless deflection increases with the decrease of scale. In addition, transverse load q and the functional gradient index m also have a significant impact on the distribution of electric potential. This paper will provide useful theoretical guidance for the design of micro-sensors and micro-actuators.http://www.sciencedirect.com/science/article/pii/S1110016824011839Flexoelectric effectPiezoelectric effectFunctional gradient microbeamNonlinear behaviorsForced vibration |
| spellingShingle | Lichang Shan Guangchun Xiao Anqing Li Shasha Zhou Li Wang Weiguang Su Yonglong Liu Lei Yang Xiaoyue Song Nonlinear forced vibration of the FGM piezoelectric microbeam with flexoelectric effect Alexandria Engineering Journal Flexoelectric effect Piezoelectric effect Functional gradient microbeam Nonlinear behaviors Forced vibration |
| title | Nonlinear forced vibration of the FGM piezoelectric microbeam with flexoelectric effect |
| title_full | Nonlinear forced vibration of the FGM piezoelectric microbeam with flexoelectric effect |
| title_fullStr | Nonlinear forced vibration of the FGM piezoelectric microbeam with flexoelectric effect |
| title_full_unstemmed | Nonlinear forced vibration of the FGM piezoelectric microbeam with flexoelectric effect |
| title_short | Nonlinear forced vibration of the FGM piezoelectric microbeam with flexoelectric effect |
| title_sort | nonlinear forced vibration of the fgm piezoelectric microbeam with flexoelectric effect |
| topic | Flexoelectric effect Piezoelectric effect Functional gradient microbeam Nonlinear behaviors Forced vibration |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824011839 |
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