Liu Yun Fei, Wang Yan Qing
Department of Mechanics, College of Sciences, Northeastern University, Shenyang 110819, China.
Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, China.
Nanomaterials (Basel). 2019 Feb 20;9(2):301. doi: 10.3390/nano9020301.
In this work, we aim to study free vibration of functionally graded piezoelectric material (FGPM) cylindrical nanoshells with nano-voids. The present model incorporates the small scale effect and thermo-electro-mechanical loading. Two types of porosity distribution, namely, even and uneven distributions, are considered. Based on Love's shell theory and the nonlocal elasticity theory, governing equations and corresponding boundary conditions are established through Hamilton's principle. Then, natural frequencies of FGPM nanoshells with nano-voids under different boundary conditions are analyzed by employing the Navier method and the Galerkin method. The present results are verified by the comparison with the published ones. Finally, an extensive parametric study is conducted to examine the effects of the external electric potential, the nonlocal parameter, the volume fraction of nano-voids, the temperature rise on the vibration of porous FGPM cylindrical nanoshells.
在这项工作中，我们旨在研究具有纳米孔隙的功能梯度压电材料（FGPM）圆柱形纳米壳的自由振动。本模型考虑了小尺度效应和热 - 电 - 机械载荷。考虑了两种孔隙率分布类型，即均匀分布和不均匀分布。基于洛夫壳理论和非局部弹性理论，通过哈密顿原理建立了控制方程和相应的边界条件。然后，采用纳维方法和伽辽金方法分析了不同边界条件下具有纳米孔隙的FGPM纳米壳的固有频率。通过与已发表结果的比较验证了本研究结果。最后，进行了广泛的参数研究，以考察外部电势、非局部参数、纳米孔隙体积分数、温度升高对多孔FGPM圆柱形纳米壳振动的影响。
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