## 1 Introduction  
Functionally graded materials (FGMs) are well-known to be designed and produced for thermal protection of high-speed spacecrafts, ships and underwater vessels due to their outstanding mechanical properties. Nowadays, FGMs have been adopted in modern applications such as aircraft, civil engineering and other structures in thermal conditions with high temperatures. Hence, the investigation of their mechanical behavior, such as the vibration of FGM structures, is of great interest for structural designers even in a nonlocal sense. [PERSON] et al. [1] presented a nonlinear finite element approach to FG circular plates with a modified couple stress theory (MCST) and the first-order shear deformation theory (FSDT) to study their deflection response. [PERSON] et al. [2] analyzed the stability and vibration of three-layered conical shells with a FGM layer subjected to an axial compressive load. A novel sinusoidal shear deformation theory for bending, buckling and vibration of FG plates was developed by [PERSON] and [PERSON] [3], involving a sinusoidal distribution of transverse shear stresses, with only four unknowns, differently from conventional sinusoidal shear deformation theories. At the same time, [PERSON] et al. [4] studied the thermal effect on the free vibration response of FG truncated conical shell panels while applying the Hamiltonian principle and FSDT to determine the governing equations of motion. [PERSON] and [PERSON] [5] proposed a semianalytical solution for the natural frequencies of thick FG plates resting on an elastic foundation. [PERSON] et al. [6] studied the free vibration response of functionally graded piezoelectric (FGP) annular plates based on a 3D elasticity, where a reduced sensitivity of thinner plates to the FGM volume fraction index and boundary conditions was found. In another paper, [PERSON] et al. [7] carried out a size-dependent buckling analysis of FG microbeams by means of a modified couple stress theory. Sandwich constructions with thin facesheets and lightweight cores are largely applied in aircraft, aviation, satellites and naval applications because of their specific lightweight, stiffness and fatigue resistance. Recently, annular sandwich plates were used as structural elements in primary structures of an aircraft/helicopter, such as floor panels, wings, ailerons and rotor blades. To use them, a good knowledge of their constructional properties and dynamic behavior is crucial. [PERSON] et al. [8] developed a biaxial buckling analysis of soft-core composite sandwich plates using an improved higher-order theory. In this work, a third-order plate theory was applied to model facesheets, whereas quadratic and cubic functions were considered for an accurate description of the transverse and in-plane displacements of the core. The governing equations and boundary conditions were derived by applying the principle of minimum potential energy. A refined zigzag theory was employed by [PERSON] et al. [9] for the study of the vibration response of viscoelastic functionally graded carbon nanotube-reinforced composite (FG-CNTRC) microplates with piezoelectric layers. The Kelvin-Voigt model was used to present a realistic sandwich microplate immersed within a magnetic and electric field together with an orthotropic visco-Pasternak foundation. The governing equations of the problem were developed using the Hamiltonian principle, and they were solved using a Navier-type solution. The results showed a meaningful effect of the volume fraction on the natural frequency response of the structure, controlled by the electric and magnetic parameters. [PERSON] et al. [10] discussed the structural modeling, vibration study and optimal viscoelastic layer characterization of adaptive sandwich beams with an electrorheological fluid (ERF) core, based on Timoshenko beam theory. [PERSON] et al. [11] analyzed the aeroelastic dynamic stability of rotating annular sandwich plates with a viscoelastic core layer.