Acta Mechanica

, Volume 229, Issue 6, pp 2379–2392 | Cite as

Flexoelectric effect on vibration responses of piezoelectric nanobeams embedded in viscoelastic medium based on nonlocal elasticity theory

  • D. P. Zhang
  • Y. J. Lei
  • S. Adhikari
Original Paper


In this study, vibration characteristics of a piezoelectric nanobeam embedded in a viscoelastic medium are investigated based on nonlocal Euler–Bernoulli beam theory. In doing this, the governing equations of motion and boundary conditions for vibration analysis are first derived using Hamilton’s principle, where nonlocal effect, piezoelectric effect, flexoelectric effect, and viscoelastic medium are considered simultaneously. Subsequently, the transfer function method is employed to obtain the natural frequencies and corresponding mode shapes in closed form for the embedded piezoelectric nanobeam with arbitrary boundary conditions. The proposed mechanics model is validated by comparing the obtained results with those available in the literature, where good agreement is achieved. The effects of nonlocal parameter, boundary conditions, slenderness ratio, flexoelectric coefficient, and viscoelastic medium on vibration responses are also examined carefully for the embedded nanobeam. The results demonstrate the efficiency and robustness of the developed model for vibration analysis of a complicated multi-physics system comprising piezoelectric nanobeam with flexoelectric effect, viscoelastic medium, and electrical loadings.


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This research is supported by the National Natural Science Foundation of China (Grant Nos. 11272348 and 11302254).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Aerospace Science and EngineeringNational University of Defense TechnologyChangshaChina
  2. 2.College of EngineeringSwansea University, Bay CampusSwanseaWales, UK

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