Free vibration behavior of an elliptical sandwich microplate, consisting of a saturated porous core and two piezoelectric face layers, standing on an elastic foundation

Multi-layer sandwich panels are lightweight and stable structures with high stiffness and the ability to absorb energy. They have numerous applications, e.g., controlling the vibration and buckling of structures. Previously, studies have been performed on sandwich rectangular and circular structures. Given the complexities, the vibration behavior of elliptical structures in microdimensions has not yet been studied. This article reports, novel and theoretical findings on the free vibration behavior of an elliptical microplate. The structure was analyzed based on the first-order shear deformation theory. It consisted of a 3-layer elliptical microplate with a porous core and two piezoelectric face layers, standing on a Winkler-Pasternak elastic foundation. We used Hamilton's principle and Galerkin's method to solve the governing equations. The core's predetermined porosities were distributed either monotonously, symmetrically or asymmetrically. The proposed variables satisfied the requirements for the vibration analyses of the structure under clamped boundary condition. The data validity was confirmed against the available literature. We found that increasing the microplate's thickness leads to a rising or declining trend in the natural vibration frequency, regardless of the core's thickness. The results indicate that variations in the porosity and Skempton's coefficients mildly affect the structure's vibration frequencies. The highest and lowest frequency variations occur when the core's porosity is symmetrical and monotonous, respectively. Variations in the coefficients of the elastic foundation increase the microplate's natural vibration frequency. The structure's frequency is maximum when standing on a Winkler-Pasternak foundation, but the frequency exhibits a significant decline when the foundation is absent.