Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite is the objective of this study. The nanocomposite is exposed to electric voltage and external parametric excitation. First, a functionally graded porous core nanoplate is modeled and then two piezoelectric layers are glued with core. It is also rested on a visco-Pasternak foundation. Second, to derive governing equation of motion, two theories including Mindlin and Kirchhoff plate theories and Hamilton’s principle are utilized. In the next step, to obtain and solve ordinary differential equation, Galerkin technique and multiple time scales method are used, respectively. At the end, modulation equation of piezoelectric/functionally graded porous nanocomposite for both primary and secondary resonances is obtained and discussed. Emphasizing the effect of piezoelectric and flexoelectric, von Karman nonlinear deformation and parametric external excitation are simultaneously taken into account. It is found that electric voltage has no effect on the performance of piezoelectricity and flexoelectricity of the material on vibration behavior. The results of this study can be useful as benchmark for the next investigations in field of energy harvesting systems and piezoelectric structures.

中文翻译：

---

粘弹性基础上压电/功能梯度多孔纳米复合材料非线性受迫振动的挠曲电效应研究

本研究的目的是研究挠曲电效应对压电/功能梯度多孔纳米复合材料的非线性强迫振动。纳米复合材料暴露于电压和外部参数激发。首先，对功能梯度多孔核纳米板进行建模，然后将两个压电层与核粘合。它也建立在粘滞帕斯捷尔纳克基础上。其次，为了推导运动控制方程，利用了Mindlin和Kirchhoff板理论和Hamilton原理这两种理论。下一步，分别采用伽辽金法和多时间尺度法求解常微分方程。在最后，获得并讨论了用于初级和次级共振的压电/功能梯度多孔纳米复合材料的调制方程。强调压电和挠曲电效应，同时考虑von Karman非线性变形和参数外部激励。发现电压对材料的压电性能和挠曲电性能对振动行为没有影响。这项研究的结果可用作能量收集系统和压电结构领域的下一步研究的基准。发现电压对材料的压电性能和挠曲电性能对振动行为没有影响。这项研究的结果可用作能量收集系统和压电结构领域的下一步研究的基准。发现电压对材料的压电性能和挠曲电性能对振动行为没有影响。这项研究的结果可用作能量收集系统和压电结构领域的下一步研究的基准。