Advances in nano research

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Propagating and evanescent waves in a functionally graded nanoplate based on nonlocal theory

  • Cancan Liu (School of Mechanical and Power Engineering, Henan Polytechnic University) ;
  • Jiangong Yu (School of Mechanical and Power Engineering, Henan Polytechnic University) ;
  • Bo Zhang (School of Mechanical and Power Engineering, Henan Polytechnic University) ;
  • Xiaoming Zhang (School of Mechanical and Power Engineering, Henan Polytechnic University) ;
  • Xianhui Wang (School of Mechanical and Power Engineering, Henan Polytechnic University)
  • Received : 2022.02.05
  • Accepted : 2022.07.08
  • Published : 2023.05.25
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Abstract

The purpose of this paper is to present the analysis of propagating and evanescent waves in functionally graded (FG) nanoplates with the consideration of nonlocal effect. The analytical integration nonlocal stress expansion Legendre polynomial method is proposed to obtain complete dispersion curves in the complex domain. Unlike the traditional Legendre polynomial method that expanded the displacement, the presented polynomial method avoids employing the relationship between local stress and nonlocal stress to construct boundary conditions. In addition, the analytical expressions of numerical integrations are presented to improve the computational efficiency. The nonlocal effect, inhomogeneity of medium and their interactions on wave propagation are studied. It is found that the nonlocal effect and inhomogeneity of medium reduce the frequency bandwidth of complex evanescent Lamb waves, and make complex evanescent Lamb waves have a higher phase velocity at low attenuation. The occurrence of intersections of propagating Lamb wave in the nonlocal homogeneous plate needs to satisfy a smaller Poisson's ratio condition than that in the classical elastic theory. In addition, the inhomogeneity of medium enhances the nonlocal effect. The conclusions obtained can be applied to the design and dynamic response evaluation of composite nanostructures.

Keywords

Acknowledgement

The authors gratefully acknowledge the support by the National Natural Science Foundation of China (No. 51975189 and No.12102131), the Project funded by China Postdoctoral Science Foundation under grant numbers 2021M701102.

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