<p>The vibration characteristics of piezo-electromagnetic annular plates with hierarchical auxetic including (hierarchical diamond and hierarchical square) and porous cores via Chebyshev-Ritz method for various boundary conditions were investigated. Various porosity patterns such as increasing porosity distribution from the outer edge to the inner edge (<i>P</i>₁), from the inner edge to the outer edge (<i>P</i>₂), and uniform distribution (<i>P</i>₃), have been investigated for the core of the sandwich structure. The effect of various parameters including the facesheet to core thickness ratio, three types porous distribution, porosity parameter, weight fraction of Graphene platelets (GPLs), aspect ratio, thickness of graphene platelets, three types piezo materials, two types auxetic core, and different types of boundary conditions on the natural frequency of an annular sandwich plate was examined. The novelty of this work includes the study of the hierarchical diamond and square cores for a piezo-electric and piezo-magnetic annular plate, and also, the survey of the effective core parameters such as the thickness to characteristic length <i>t</i>/<i>L</i> (<i>a</i>₁), the semi-diameter of the tetragonal cell to the characteristic length ratio <i>r</i>/<i>L</i> (<i>a</i>₂) on the natural frequency was considered. The results show that the wave number increases the frequency. Also, a structure with a porous <i>P</i>₂ core and piezo-electromagnetic layers has the highest stiffness and frequency in comparison to the other structures. These structures in vibration control and energy harvesting applications were utilized. These smart structures are widely used in aerospace, robotics, and noise absorption systems.</p>