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This paper deals with wave propagation and vibration of a porous beam embedded via nanocomposite piezoelectric layers. Various patterns of reinforcement of the face sheets by non-uniform graphene nanoplatelets (GPLs) are considered through modified Halpin-Tsai micromechanics model to approximate the Young modulus and Poisson's ratio of graphene/piezoelectric polymer layers. The sandwich's face sheets, due to their characteristics, are regarded as sensor and actuator with which the wave velocity and frequency of structure can be controlled and for this reason, a proportional-differential (PD) controller is handled. So as to model the structure much more realistic, the material characteristic of whole system are hypothesized as viscoelastic state according to Kelvin-Voigt model and Kerr viscoelastic foundation is developed which include two springs, two dampers and one shear elements as well. For …