The sandwich structures contain three or more layers attached to the core. In the current research, a three-layered sandwich microplate containing functionally graded (FG) porous materials as core and piezoelectric nanocomposite materials as face sheets subjected to electric field resting on Pasternak foundation is chosen as a model to investigate its vibrational behavior. To make the face sheets stiffer, they are reinforced by carbon nanotubes (CNTs) via different distribution patterns which result in changing their properties along the thickness direction. An innovative quasi-3D shear deformation theory with five unknowns, Hamilton’s principle, and modified couple stress theory are hired to gain equations of motion related to the abovementioned microstructure. Eventually, the evaluation of materials’ properties, geometry specifications, foundation moduli, and hygrothermal environment on vibrational behavior of such structures became easier using the presented results of the current study in figure format. As an instance, it is revealed that CNTs’ volume fraction elevation causes mechanical properties improvement, and in the following, natural frequency increment. Besides, considering the hygrothermal environment causes significant effects on the results.

夹层结构包含附着在芯上的三层或更多层。在当前的研究中，选择三层夹心微孔板作为模型研究其振动行为，该三层夹心微孔板以功能梯度（FG）多孔材料为核心，压电纳米复合材料为面板，在电场作用下置于Pasternak基础上。为了使面板更坚硬，它们通过碳纳米管（CNT）通过不同的分布方式进行了加固，从而导致其厚度方向上的特性发生了变化。利用具有五个未知数的创新准3D剪切变形理论，汉密尔顿原理和修正偶应力理论来获得与上述微结构有关的运动方程。最终，评估材料的特性，几何规格，使用当前研究的图形形式的结果，基础模量和湿热环境对此类结构的振动行为的影响变得更加容易。作为一个实例，揭示了CNT的体积分数升高引起机械性能的改善，并且随后引起固有频率的增加。此外，考虑湿热环境会对结果产生重大影响。