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Theoretical study of elastic wave propagation through a functionally graded micro-structured plate base on the modified couple-stress theory

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Abstract

In this paper, two different methods, Legendre orthogonal polynomial method (LOPM) and Global matrix method (GMM), are combined with the couple-stress theory to investigate the reflection and transmission of P wave in a functionally graded (FG) couple-stressed plate immersed in liquid. The GMM needs to divide the FG plate into the multilayered model, with each layer containing six partial waves. However, the LOPM only expands the displacement vectors in the FG couple-stressed plate into the Legendre orthogonal polynomial series. The paper shows that both methods are in good agreement. Nevertheless, the proposed LOPM is more efficient for the FG microstructure because it does not require plate delamination and calculation of the displacements of each partial wave. It also shows that the couple-stress effect affects the resonant frequencies of the FG plate, decreasing the number of resonant frequencies. By controlling the gradient field, some resonances can be avoided.

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Acknowledgement

The authors gratefully acknowledge the support by the National Natural Science Foundation of China (Nos. U1804134 and 51975189), the Key Scientific and Technological Project of Henan Province (Nos. 192102210189 and 182102210314) and the Training Plan of Young Key Teachers of Universities in Henan Province (No. 2018-GGJS-060).

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Authors and Affiliations

  1. School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, 454003, People’s Republic of China

    Cancan Liu, Jiangong Yu, Xiaoming Zhang & Bo Zhang

  2. CNRS, Univ. Lille, YNCREA, Centrale Lille, UMR 8520 – IEMN, DOAE, University of Polytechnique Hauts-de-France, 59313, Valenciennes, France

    Weijiang Xu

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  1. Cancan Liu
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  2. Jiangong Yu
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  3. Weijiang Xu
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  4. Xiaoming Zhang
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  5. Bo Zhang
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Correspondence to Xiaoming Zhang.

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Liu, C., Yu, J., Xu, W. et al. Theoretical study of elastic wave propagation through a functionally graded micro-structured plate base on the modified couple-stress theory. Meccanica 55, 1153–1167 (2020). https://doi.org/10.1007/s11012-020-01156-8

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