Naderi Ali, Quoc-Thai Tran, Zhuang Xiaoying, Jiang Xiaoning
Department of Mechanical and Aerospace Engineering, Syracuse University, Syracuse, NY 13244, USA.
Fluid Dynamics and Solid Mechanics, T-3, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
Materials (Basel). 2023 Apr 30;16(9):3485. doi: 10.3390/ma16093485.
In this study, for the first time, free and forced vibrational responses of a unimorph nanobeam consisting of a functionally graded base, along with a dielectric layer of both piezoelectricity and flexoelectricity, is investigated based on paradox-free local/nonlocal elasticity. The formulation and boundary conditions are attained by utilizing the energy method Hamilton's principle. In order to set a comparison, the formulation of a model in the framework of differential nonlocal is first presented. An effective implementation of the generalized differential quadrature method (GDQM) is then utilized to solve higher-order partial differential equations. This method can be utilized to solve the complex equations whose analytic results are quite difficult to obtain. Lastly, the impact of various parameters is studied to characterize the vibrational behavior of the system. Additionally, the major impact of flexoelectricity compared to piezoelectricity on a small scale is exhibited. The results show that small-scale flexoelectricity, rather than piezoelectricity, is dominant in electromechanical coupling. One of the results that can be mentioned is that the beams with higher nonlocality have the higher voltage and displacement under the same excitation amplitude. The findings can be helpful for further theoretical as well as experimental studies in which dielectric material is used in smart structures.
在本研究中，首次基于无悖论的局部/非局部弹性理论，对由功能梯度基底以及兼具压电性和挠曲电效应的介电层组成的单压电晶片纳米梁的自由振动和强迫振动响应进行了研究。通过运用能量法哈密顿原理得到了公式和边界条件。为了进行比较，首先给出了微分型非局部框架下模型的公式。然后利用广义微分求积法（GDQM）的有效实现来求解高阶偏微分方程。该方法可用于求解解析结果很难得到的复杂方程。最后，研究了各种参数的影响以表征系统的振动行为。此外，展示了在小尺度下挠曲电效应相比于压电效应的主要影响。结果表明，在机电耦合中，小尺度挠曲电效应而非压电效应占主导。可以提及的一个结果是，在相同激励幅度下，非局部性较高的梁具有更高的电压和位移。这些发现有助于在智能结构中使用介电材料的进一步理论和实验研究。
