Journal of Elasticity

, Volume 130, Issue 2, pp 197–210 | Cite as

Wave Propagation in Flexoelectric Microstructured Solids

  • Taotao Hu
  • Wenjun Yang
  • Xu Liang
  • Shengping Shen


Wave propagation in elastic dielectrics with flexoelectricity, micro-inertia and strain gradient elasticity is investigated in this paper. Dispersion phenomenon, which does not exist in classical elastic dielectric theory, is observed in the flexoelectric microstructured solids. Analytical solutions for the phase velocity \(C_{p}\), group velocity \(C_{g}\) and their ratio \(\gamma = C_{g} / C_{p}\) are calculated for the case of harmonic decomposition. The magnitudes of the phase velocity and group velocity changed with the increasing of the wave number, while they are constant in the classical elastic dielectric theory. It is shown that the flexoelectricity, micro-inertia and microstructural effects are significant to predict the real behavior of longitudinal wave propagating in flexoelectric microstructured solids. Microstructural effects are not sufficient for dealing with realistic dispersion curves in flexoelectric solids, the micro-inertia and flexoelectricity are needed to obtain a physically acceptable value of the phase and group velocities.


Wave propagation Flexoelectricity Micro-inertia Microstructure effects 

Mathematics Subject Classification

74F99 74J10 



This work was supported by the National Natural Science Foundation of China (Grants Nos. 11372238, 11302161, 11302162 and 11602189) and the Chang Jiang Scholar program. The support from the China Postdoctoral Science Foundation (Grant No. 2015M580835) and the Fundamental Research Funds for the Central Universities was also appreciated.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.State Key Laboratory for Strength and Vibration of Mechanical StructuresXi’an Jiaotong UniversityXi’anP.R. China

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