Abstract <p>The progress of various industries, especially the transportation industry, depends on the materials and structures required by these industries. With the emergence of metamaterials, one of the challenges for researchers is to investigate the effect of these materials on various structures. This research investigates the vibration behavior of a sandwich plate with piezo-electro-magnetic face sheets and the effect of several core models (three types of porous and two types of auxetic cores). The equations of motion for the sandwich plate are determined. These equations are solved using a semi-analytical method, and the vibration of the sandwich plate is obtained. The effects of porosity distribution, electric and magnetic fields, different parameters of the auxetic core, and thickness ratio on the natural frequency are determined. The results show that the effect of the 3rd type of porous distribution on the structure frequency is more than that of other porous distributions. The effect of auxetic cores with negative Poisson’s ratios was also analyzed. The second type of the auxetic core has a more significant effect on the frequency. The findings of this study have practical applications in the aerospace sector and can be used in developing lightweight structures, sensors, and actuators.</p>