This article introduces a computational means for investigating the electroelastic nonlinear wave dispersion traits of the nano-dimension sandwich pipe, which is composed of a core formed of a bi-directional functionally graded (Bi-FG) material, together with a piezoelectric sensor/actuator. A combination of Hamilton’s principle, first-order shear deformation, along with Von-Karman nonlinearity, is used for modeling and obtaining the nonlinear governing equations of the nano-sized sandwich pipe connected to a piezoelectric part. The nonlinear governing equations to obtain the nonlinear phase velocity of the current system are determined using a combination of analytical and multiple scales approaches. Due to some computational cost for choosing the precise values of both the nonlocality factor and length scale of the nanopipe in the laboratory, for the first time in this research, with the aid of COMSOL multi-physics finite element simulation, the results are verified, and new outcomes for obtaining the exact functions for nonlocal and length scale factors is presented. In addition, an artificial neural network (ANN) is utilized in this study for the prediction of the results. The mathematical and finite element results were used to train the ANN. A newly presented optimization algorithm is exploited for the first time for optimizing the ANN parameters concluding higher accuracy of the ANN predictions. Consequently, to explore the influences of the location of the piezoelectric patch, nonlocality and length scale factors, and applied voltage parameter on the phase velocity characteristics of the nano-dimension sandwich pipe made of a Bi-FG core and electrically patch, an effort is performed. As an applicable result that can be useful in the related nano-industries, the current work presents exact nonlocal and length scale functions for different conditions.

中文翻译：

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通过非局部应变梯度理论研究旋转压电 NEMS 传感器/执行器中的电弹性波色散

本文介绍了一种用于研究纳米尺寸夹层管电弹性非线性波色散特性的计算方法，该夹层管由双向功能梯度（Bi-FG）材料形成的核心以及压电传感器/执行器组成。结合哈密顿原理、一阶剪切变形和冯卡门非线性，对连接到压电部件的纳米级夹层管的非线性控制方程进行建模和获得。使用解析和多尺度方法的组合来确定获得当前系统的非线性相速度的非线性控制方程。由于在实验室中选择纳米管的非定域因子和长度尺度的精确值需要一定的计算成本，本研究首次借助COMSOL多物理场有限元模拟对结果进行了验证，并提出了获得非局部和长度尺度因子的精确函数的新结果。此外，本研究还利用人工神经网络（ANN）来预测结果。数学和有限元结果用于训练人工神经网络。首次利用新提出的优化算法来优化 ANN 参数，从而提高 ANN 预测的准确性。因此，为了探讨压电贴片的位置、非定域性和长度尺度因子以及施加电压参数对由Bi-FG磁芯和电贴片制成的纳米尺寸夹层管的相速度特性的影响，我们做了以下努力：执行。作为可用于相关纳米工业的适用结果，当前的工作提出了不同条件下的精确非局部和长度尺度函数。