## 1 Introduction
Utilizing the sampling surfaces approach, [PERSON] and [PERSON] [23] investigated the 3D coupled steady-state thermomechanical behavior of a simply supported FG piezoelectric laminated plate under thermal loading analytically. Based on the Lord-Sublman formulation and utilizing DQM and a multi-step time integration scheme, the thermoelastic response of FG cylindrical panels bonded with piezoelectric layers and subjected to thermal shock was investigated by [PERSON] et al. [24]. Using the meshless methods and third-order shear deformation theory, [PERSON] and [PERSON] [25] analyzed thermo-electro-mechanic behaviors of the sandwich FG plate attached to piezoelectric layers in the framework of HSDT. Using a sandwich nanobeam model, the electromechanical response of a piezoelectric energy harvester under compressive axial load was considered by [PERSON] et al. [26] for both prebuckling and postbuckling states, utilizing the Galerkin technique and the harmonic balance method. [PERSON] and [PERSON] [27] investigated the thermo-viscoelastic behavior of beams made of FG piezoelectric material (FGPM) using the Airy stress function based on elasticity theory. [PERSON] et al. [28] considered the effect of viscoelastics at the interface on the damping and thermomechanical response of composite rectangular plates. The thermo-viscoelastic response of 3D woven composite was investigated by [PERSON] and [PERSON] [29] using the finite element method and the Prony series. [PERSON] and [PERSON] also investigated the bending of viscoelastic cylindrical panels under uniform pressure within the framework of 3D elasticity theory and using SS-DQM [30]. [PERSON] et al. [31] used [PERSON]'s approach to study the damped vibration response of the viscoelastic corrugated nanoplates within the framework of FSDT and utilizing the Kelvin-Voigt model. The time-dependent response of FG sandwich plates with a viscoelastic core was presented analytically by [PERSON] et al. [32] using the standard linear solid model of viscoelasticity and using the Laplace transformation technique. Utilizing a meshless local Petrov-Galerkin technique and considering thermo-mechanical loads, an exact solution for thermo-viscoelastic behaviors of fiber-reinforced polymer composites was performed by [PERSON] and [PERSON] [33] using viscoelastic constitutive equations. The exact solution for active control performance, vibration dampening, and aeroelastic behavior of simply supported FG-GPLR composite plates bonded with piezoelectric patches as sensors and actuators under supersonic airflow was examined by [PERSON] et al. [34]. The above-mentioned survey found that the bending of rectangular FG viscoelastic plates embedded in piezoelectric layers subjected to electro-thermal loading has not been reported in the literature. To this end, this article is dedicated to the analysis of the thermo-viscoelastic response of the sandwich plate with a viscoelastic core and two surrounding piezoelectric face-layers simultaneously exposed to electro-thermal loading based on 3D elasticity theory to determine the results with the highest level of accuracy. Mechanical properties of the FGM viscoelastic layer are assumed to obey the transverse coordinate power law function. The constitutive equations of viscoelastic material are stated by means of the Boltzmann superposition principle. Then, based on the theory of elasticity, the governing equations in three dimensions are solved analytically in the Laplace domain by means of SS-FSM. Finally, the solution in the time domain is derived by applying the inverse Laplace to the obtained equations. After validation of the present formulation, the effects of geometric dimension, electro-thermal loads, boundary conditions, and viscoelastic parameters on the thermo-elastic response of this smart structure are studied.