A micro scale Timoshenko beam model for piezoelectricity with flexoelectricity and surface effects
A micro scale Timoshenko beam model for piezoelectricity with flexoelectricity and surface effects
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DOI：
10.1016/j.compstruct.2015.09.046
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发表时间：
2016-02
影响因子：
6.3
通讯作者：
Y. Yue;K. Xu;T. Chen
中科院分区：
文献类型：
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作者：
Y. Yue;K. Xu;T. Chen
提出了一种微尺度压电梁结构，该梁具有挠曲电和表面效应。利用变分原理和汉密尔顿原理，得到了控制方程和相应的边界条件。由于考虑了剪切应变的影响，考虑了剪切应变梯度引起的弯电效应，使新模型更具有一般性。基于该模型，分别求解了简支压电纳米梁在均布载荷作用下的静弯曲和自由振动问题。数值结果表明，弯电效应和表面效应对梁的变形都有显著的影响。如果只考虑挠曲电效应，理论预测与实验结果可能会有很大差异。剪切应变梯度对静弯曲问题的机电响应也有很大的影响。此外，表面性质的改变不仅直接影响梁的静态弯曲，而且显著地改变梁的固有频率。该研究为压电纳米梁的分析提供了指导，也有助于理解材料特性如何影响纳米梁的机电响应。
A micro scale Timoshenko beam is developed for the piezoelectricity with flexoelectricity and surface effects. By virtue of the variational principle and Hamilton’s principle, the governing equations and related boundary conditions are obtained. As the shear strain is involved for the Timoshenko beam, the flexoelectric effect induced by the shear strain gradient is considered to make the new model more general. Based on this new Timoshenko beam model, the static bending and free vibration problems of a simply supported piezoelectric nanobeam with uniform load applied are solved respectively. The numerical results reveal that both the flexoelectricity and surface effects have remarkable influence on the deformations of the beam. Only flexoelectricity considered may cause a big difference between the theoretical prediction and the experiment results. The shear strain gradient also has considerable effect on the electromechanical response of static bending problem. Moreover, the change of surface properties not only directly affects the static bending but also significantly changes the natural frequency of the beam. This study provides a guideline for the analysis of piezoelectric nanobeam, and also is helpful to understand how the material characteristics affect the electromechanical response of nanobeam.