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Advances in Nano Research Volume 13, Number 5, November 2022 , pages 465-474 DOI: https://doi.org/10.12989/anr.2022.13.5.465 |
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Guided waves of porous FG nanoplates with four edges clamped |
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Jing-Lei Zhao, Gui-Lin She, Fei Wu, Shu-Jin Yuan, Ru-Qing Bai, Hua-Yan Pu and Shilong Wang and Jun Luo
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| Abstract | ||
| Based on the nonlocal strain gradient (NSG) theory and considering the influence of moment of inertia, the governing equations of motion of porous functionally graded (FG) nanoplates with four edges clamped are established; The Galerkin method is applied to eliminate the spatial variables of the partial differential equation, and the partial differential governing equation is transformed into an ordinary differential equation with time variables. By satisfying the boundary conditions and solving the characteristic equation, the dispersion relations of the porous FG strain gradient nanoplates with four edges fixed are obtained. It is found that when the wave number is very small, the influences of nonlocal parameters and strain gradient parameters on the dispersion relation is very small. However, when the wave number is large, it has a great influence on the group velocity and phase velocity. The nonlocal parameter represents the effect of stiffness softening, and the strain gradient parameter represents the effect of stiffness strengthening. In addition, we also study the influence of power law index parameter and porosity on guided wave propagation. | ||
| Key Words | ||
| functionally graded material; guided wave; nanoplates; nonlocal strain gradient theory; porous nanomaterials | ||
| Address | ||
| Jing-Lei Zhao, Gui-Lin She, Fei Wu, Shu-Jin Yuan, Ru-Qing Bai, Hua-Yan Pu and Shilong Wang and Jun Luo: College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044, China | ||