The original formulation of the quasi-3D sinusoidal shear deformation plate theory (SSDPT) is here extended to the wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects. The sandwich structure contains a single layered graphene sheet as core integrated with zinc oxide layers as sensors and actuators. The single layered graphene sheet and zinc oxide layers are subjected, respectively, to 2D magnetic and 3D electric fields. Structural damping and surface effects are assumed using Kelvin–Voigt and Gurtin–Murdoch theories, respectively. The system is rested on an elastic medium which is simulated with a novel model namely as orthotropic visco-Pasternak foundation. An exact solution is applied in order to obtain the frequency, cut-off and escape frequencies. A displacement and velocity feedback control algorithm is applied for the active control of the frequency through a closed-loop control with bonded distributed zinc oxide sensors and actuators. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, magnetic field, viscoelastic foundation, surface stress, applied voltage, velocity feedback control gain and structural damping on the wave propagation behavior of nanostructure. Results depict that with increasing the structural damping coefficient, frequency significantly decreases.