In this paper, the free vibration characteristics of stiffened sandwich plates with auxetic core and functionally graded piezoelectric face sheet are investigated. The sandwich plate configuration comprises three distinct layers: a top layer consisting of functionally graded piezoelectric material (FGPie), a core layer composed of auxetic material exhibiting a negative Poisson's ratio, and a bottom layer made of functionally graded material (FGM). The sandwich plate is reinforced by isotropic stiffeners along the x and y directions. A novel model is established based on the four-variable shear deformation refined plate theory and the pb2-Ritz method. This model offers the flexibility to analyze plates with diverse mechanical boundary conditions and supports two types of electrical boundary conditions: closed circuit and open circuit. The accuracy and convergence of the proposed model are validated through comparative analyses against published results, thereby confirming the reliability when analyzing the vibration characteristics of this complex sandwich structure. Furthermore, some new investigations are carried out to explore the influence of various parameters on the vibrational characteristics of the stiffened piezoelectric auxetic sandwich (SA-FGPie) plates. The results suggest that the properties of the reinforcing stiffeners, such as quantity or dimensions, alter the free vibration characteristics of the SA-FGPie plates significantly. In addition, parameters such as the volume fraction indexes of the FGPie and FGM layers, electrical boundary conditions or FGPie layer thickness, as well as geometric parameters of the auxetic unit cell also have a significant influence on the vibration response of SA-FGPie plates. However, the influence of these parameters depends on the specific boundary conditions.

本文研究了带有拉胀芯和功能梯度压电面板的加筋夹层板的自由振动特性。夹层板配置包括三个不同的层：由功能梯度压电材料（FGPie）组成的顶层，由具有负泊松比的拉胀材料组成的核心层，以及由功能梯度材料（FGM）制成的底层。夹层板沿x和y方向由各向同性加劲肋加固。基于四变量剪切变形精化板理论和pb2 -Ritz方法建立了新的模型。该模型可以灵活地分析具有不同机械边界条件的板，并支持两种类型的电气边界条件：闭路和开路。通过与已发表的结果进行比较分析，验证了所提出模型的准确性和收敛性，从而证实了分析这种复杂夹层结构振动特性时的可靠性。此外，还进行了一些新的研究，以探索各种参数对加筋压电拉胀夹层（SA-FGPie）板振动特性的影响。结果表明，加强筋的属性（例如数量或尺寸）会显着改变 SA-FGPie 板的自由振动特性。此外，FGPie和FGM层的体积分数指数、电边界条件或FGPie层厚度以及拉胀晶胞的几何参数等参数也对SA-FGPie板的振动响应有显着影响。然而，这些参数的影响取决于具体的边界条件。