Size-dependent nonlinear bending and vibration of flexoelectric nanobeam based on strain gradient theory
Size-dependent nonlinear bending and vibration of flexoelectric nanobeam based on strain gradient theory
复制标题
基于应变梯度理论的柔性电纳米梁尺寸相关非线性弯曲和振动
DOI：
10.1088/1361-665x/ab1cfc
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发表时间：
2019-06
影响因子：
4.1
通讯作者：
Li Zongjun
中科院分区：
文献类型：
--
作者：
Zhao Xie;Zheng Shijie;Li Zongjun
本文首次研究了具有挠曲电性和表面效应的压电纳米梁的非线性弯曲和自由振动。为了考虑尺寸效应，基于应变梯度理论，建立了一个包含附加材料长度尺度参数的尺寸相关的Rehshenko纳米梁模型。由电焓变分法和汉密尔顿原理得到了控制方程和相应的边界条件。通过调整材料长度尺度参数的值，可以将现有的压电纳米梁公式转化为基于修正偶应力理论的压电纳米梁公式。采用广义微分求积法（GDQM）将控制微分方程和边界条件离散为一系列非线性代数方程组。然后用牛顿迭代法求解代数方程组。研究发现，应变梯度弹性效应、挠曲电效应、表面效应和外加电压对纳米梁的非线性力学行为有显著影响。模拟结果表明，应变梯度效应和弯电效应对纳米梁中的电场分布有很大的影响。此外，计算结果还表明，由于考虑了表面效应，挠曲电性的影响在一定程度上得到了削弱。数值分析表明，本模型可以被认为是可靠的定量研究尺寸依赖的非线性弯曲和非线性自由振动的压电纳米梁结合挠曲电和表面效应。
In this study, the nonlinear bending and free vibration of Timoshenko piezoelectric nanobeam incorporating flexoelectricity and surface effect are investigated for the first time. To take size effect into account, a size-dependent Timoshenko nanobeam model containing additional material length scale parameters is developed based on strain gradient theory. The governing equations and corresponding boundary conditions are obtained by electric enthalpy variation and Hamilton’s principle. By adjusting the values of material length scale parameters, the current Timoshenko piezoelectric nanobeam formulations can be transformed to those based on modified couple stress theory. The generalized differential quadrature method (GDQM) is employed to discretize governing differential equations and boundary conditions into a series of nonlinear algebraic equations. Then the algebraic equations are solved by using the Newton iteration method. It is found that strain gradient elastic effect, flexoelectricity, surface effect and applied electric voltage have significant influences on the nonlinear mechanical behaviors of nanobeam. Simulation results indicate that both the strain gradient effect and flexoelectric effect have considerable impacts on the electric field distribution in nanobeams. Moreover, the results also indicate that the influence of flexoelectricity is weakened to some extent due to the consideration of surface effect. The numerical analysis reveals that the present model can be considered reliable to quantitatively investigate size-dependent nonlinear bending and nonlinear free vibration of the piezoelectric nanobeam incorporating flexoelectric and surface effects.
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影响因子：
1.8
作者：
Y. Yue;Kai Xu;E. Aifantis
通讯作者：
Y. Yue;Kai Xu;E. Aifantis
影响因子：
6.3
作者：
Y. Yue;K. Xu;T. Chen
通讯作者：
Y. Yue;K. Xu;T. Chen
功能梯度材料非局部应变梯度梁的非线性弯曲和自由振动分析
DOI：
10.1016/j.ijengsci.2016.07.011
发表时间：
2016-10-01
影响因子：
6.6
作者：
Li, Li;Hu, Yujin
通讯作者：
Hu, Yujin
影响因子：
3.7
作者：
Majdoub, M. S.;Sharma, P.;Cagin, T.
通讯作者：
Cagin, T.
影响因子：
3.4
作者：
Li, Anqing;Zhou, Shenjie;Chen, Xi
通讯作者：
Chen, Xi