AbstractThis article evaluates the wave velocity of a leptadenia pyrotechnica rheological elastomer (LPRE) microbeam surrounded by micro piezoelectric and porosity of functionally graded materials' (FGMs) layers. Different models of graphene nano plates (GPLs) for reinforcing the face sheet are assumed by adopting Halpin–Tsai modified micromechanics theory to obtain the Poisson's ratio and Young modulus of the smart layer. The material properties of the whole system as a viscoelastic state are hypothesized using the Kelvin–Voigt theory. The motion final equations are gained by utilizing the theory of Timoshenko and the couple stress model. An analytical solution method is adopted for computing the velocity of wave, cutoff frequency, and escape frequency from the motion final equations. The influences of different distribution and volume percent of GPLs, FGM properties as well as gradient index, the numeral parameter of any layer, damping of structure, and exerted voltage on the velocity of wave microbeam are studied. Moreover, it has been seen that a rise in the FGM index leads to reduced phase velocity, cutoff, and escape frequencies. Meanwhile, enhancing the volume percent of GPLs increases the wave velocity of the microstructure beam.