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Band gaps in a periodic electro-elastic composite beam structure incorporating microstructure and flexoelectric effects

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Abstract

A new model for electro-elastic Bernoulli–Euler beams of centrosymmetric cubic materials is proposed, which incorporates microstructure and flexoelectric effects. The wave equations and boundary conditions are derived simultaneously through a variational approach based on Hamilton’s principle. The new beam model is then applied to predict elastic wave band gaps in a periodic electro-elastic composite beam structure. Bloch’s theorem and the transfer matrix method for periodic structures are used to solve the wave equations and determine band gaps. The current model reduces to its flexoelectric and classical elastic counterparts as special cases. To illustrate the new model, the effects of microstructure, flexoelectricity, beam thickness, unit cell length and volume fraction on band gaps are investigated through a parametric study. The numerical results show that the microstructure and flexoelectric effects lead to increased band gap frequencies, and these two effects are important when the beam thickness is at the submicron and micron scales. In addition, it is found that the unit cell length and volume fraction can significantly affect the band gap size at all length scales. These findings indicate that band gap frequencies and size can be tailored by adjusting the microstructural and material parameters.

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Acknowledgements

GYZ gratefully acknowledges the support by the National Natural Science Foundation of China (Grant No. 12002086) and Zhishan Youth Scholar Program of SEU. The authors also would like to thank Dr. Esmaeal Ghavanloo and two anonymous reviewers for their encouragement and helpful comments on an earlier version of the paper.

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Authors and Affiliations

  1. Jiangsu Key Laboratory of Engineering Mechanics, School of Civil Engineering, Southeast University, Nanjing, Jiangsu, 210096, China

    G. Y. Zhang & Z. Z. He

  2. Department of Mechanical Engineering, Lyle School of Engineering, Southern Methodist University, Dallas, TX, 75275-0337, USA

    X.-L. Gao & H. W. Zhou

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  1. G. Y. Zhang
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This paper is submitted for the Special Issue on Mechanics of Size-Dependent Materials.

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Zhang, G.Y., He, Z.Z., Gao, XL. et al. Band gaps in a periodic electro-elastic composite beam structure incorporating microstructure and flexoelectric effects. Arch Appl Mech 93, 245–260 (2023). https://doi.org/10.1007/s00419-021-02088-9

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