This investigation aims to perform a detailed natural frequency analysis of functionally graded porous beams integrated with transverse (d31) and shear (d15) piezoelectric layers under short circuit and open circuit electrical conditions. It is assumed that the core layer is made of functionally graded materials containing porosities. Due to the existence of internal pores, the mechanical properties of functionally graded materials are considered according to the modified power-law rule which includes the effect of porosity. The distribution of electric potential within the d31 and d15 piezoelectric layers is modeled based on nonlinear variation for both short circuit and open circuit conditions. Employing the classical, the first-order, and the higher-order beam theories incorporated with the virtual work principle as well as Maxwell’s equation, the electromechanical equations of motion are derived. The governing equations are then solved analytically for simply supported boundary condition and a parametric study is presented. After validation of the results, some new interesting conclusions covering the effects of porosity volume fraction, porosity distribution, various piezoelectricity modes, power-law index, and the beam theories on short circuit and open circuit resonance frequencies are reported. It is believed that the presented numerical results could provide a benchmark to check the accuracy of the approximated approaches.

中文翻译：

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基于高阶理论的横向剪切耦合压电功能梯度多孔梁的振动分析

本研究旨在对在短路和开路电气条件下与横向 (d31) 和剪切 (d15) 压电层集成的功能梯度多孔梁进行详细的固有频率分析。假设核心层由包含孔隙的功能梯度材料制成。由于内部孔隙的存在，功能梯度材料的力学性能根据修正的幂律法则来考虑，其中包括孔隙率的影响。d31 和 d15 压电层内的电势分布基于短路和开路条件下的非线性变化建模。采用经典、一阶和高阶梁理论，结合虚功原理和麦克斯韦方程，推导出运动的机电方程。然后针对简支边界条件对控制方程进行解析求解，并进行参数研究。在对结果进行验证后，报告了一些新的有趣结论，包括孔隙率体积分数、孔隙率分布、各种压电模式、幂律指数以及梁理论对短路和开路谐振频率的影响。相信所呈现的数值结果可以为检查近似方法的准确性提供基准。报告了一些新的有趣结论，涵盖孔隙率体积分数、孔隙率分布、各种压电模式、幂律指数以及梁理论对短路和开路谐振频率的影响。相信所呈现的数值结果可以为检查近似方法的准确性提供基准。报告了一些新的有趣结论，涵盖孔隙率体积分数、孔隙率分布、各种压电模式、幂律指数以及梁理论对短路和开路谐振频率的影响。相信所呈现的数值结果可以为检查近似方法的准确性提供基准。