Free vibration of nanobeams with surface and dynamic flexoelectric effects
Abstract In this paper, the free vibration of piezoelectric nanobeams considering static flexoelectric, dynamic flexoelectric, and surface effects is studied. Based on the theories of the Timoshenko beam and Euler-Bernoulli beam, a theoretical model of flexoelectric nanobeams is established and the...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-12-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-82002-9 |
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| author | Peng Wang JiaWei Xu XiWen Zhang YingHui Lv |
| author_facet | Peng Wang JiaWei Xu XiWen Zhang YingHui Lv |
| author_sort | Peng Wang |
| collection | DOAJ |
| description | Abstract In this paper, the free vibration of piezoelectric nanobeams considering static flexoelectric, dynamic flexoelectric, and surface effects is studied. Based on the theories of the Timoshenko beam and Euler-Bernoulli beam, a theoretical model of flexoelectric nanobeams is established and the governing equations and boundary conditions of this model are derived using the variational principle. Then, the analytical solution of the frequency equation is obtained by using the Navier method. Numerical results indicate that the size dependence of the dynamic flexoelectric effect is stronger than the surface effect. The surface and dynamic flexoelectric effects exhibit a competitive mechanism on the natural frequency. |
| format | Article |
| id | doaj-art-2b4c2dc586d34a15af34a5cb6ce57dea |
| institution | OA Journals |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-2b4c2dc586d34a15af34a5cb6ce57dea2025-08-20T02:20:41ZengNature PortfolioScientific Reports2045-23222024-12-0114111210.1038/s41598-024-82002-9Free vibration of nanobeams with surface and dynamic flexoelectric effectsPeng Wang0JiaWei Xu1XiWen Zhang2YingHui Lv3School of Civil Engineering and Architecture, University of JinanSchool of Civil Engineering and Architecture, University of JinanSchool of Civil Engineering and Architecture, University of JinanSchool of Civil Engineering and Architecture, University of JinanAbstract In this paper, the free vibration of piezoelectric nanobeams considering static flexoelectric, dynamic flexoelectric, and surface effects is studied. Based on the theories of the Timoshenko beam and Euler-Bernoulli beam, a theoretical model of flexoelectric nanobeams is established and the governing equations and boundary conditions of this model are derived using the variational principle. Then, the analytical solution of the frequency equation is obtained by using the Navier method. Numerical results indicate that the size dependence of the dynamic flexoelectric effect is stronger than the surface effect. The surface and dynamic flexoelectric effects exhibit a competitive mechanism on the natural frequency.https://doi.org/10.1038/s41598-024-82002-9Dynamic flexoelectricitySurface effectFlexoelectric effectPiezoelectric nanobeamFree vibration |
| spellingShingle | Peng Wang JiaWei Xu XiWen Zhang YingHui Lv Free vibration of nanobeams with surface and dynamic flexoelectric effects Scientific Reports Dynamic flexoelectricity Surface effect Flexoelectric effect Piezoelectric nanobeam Free vibration |
| title | Free vibration of nanobeams with surface and dynamic flexoelectric effects |
| title_full | Free vibration of nanobeams with surface and dynamic flexoelectric effects |
| title_fullStr | Free vibration of nanobeams with surface and dynamic flexoelectric effects |
| title_full_unstemmed | Free vibration of nanobeams with surface and dynamic flexoelectric effects |
| title_short | Free vibration of nanobeams with surface and dynamic flexoelectric effects |
| title_sort | free vibration of nanobeams with surface and dynamic flexoelectric effects |
| topic | Dynamic flexoelectricity Surface effect Flexoelectric effect Piezoelectric nanobeam Free vibration |
| url | https://doi.org/10.1038/s41598-024-82002-9 |
| work_keys_str_mv | AT pengwang freevibrationofnanobeamswithsurfaceanddynamicflexoelectriceffects AT jiaweixu freevibrationofnanobeamswithsurfaceanddynamicflexoelectriceffects AT xiwenzhang freevibrationofnanobeamswithsurfaceanddynamicflexoelectriceffects AT yinghuilv freevibrationofnanobeamswithsurfaceanddynamicflexoelectriceffects |