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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Main Authors: Peng Wang, JiaWei Xu, XiWen Zhang, YingHui Lv
Format: Article
Language:English
Published: Nature Portfolio 2024-12-01
Series:Scientific Reports
Subjects:
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.
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publisher Nature Portfolio
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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