In this paper, the concept of smart materials has been engaged in order to control and abate the vibrations of non-linear beams. In the meantime, flexural vibration of viscoelastic has been taken into account aimed at reinforcing the carbon nanotube beams. This theory has applied the viscoelastic model to draw out the classical viscoelastic Kelvin–Voigt model. Likewise, the Hamilton’s principle has been employed to derive the non-linear differential equations of beam’s motion as for the piezoelectric patches and also the multiple scales method has been engaged in order to solve the non-linear equation of system motion. A fuzzy controller has been desirably arranged in the piezoelectric actuator/sensor loop to reduce the forced vibrations for any arbitrary stimulation. Due to majestic efficiency of the Bees Algorithm (BA) in the solution of many different engineering problems, it has been engaged for this work. To ensure and confirm the robustness of the proposed approach, three different conditions of forced stimulation have been taken into account for the studied system. In all, the non-linear simulation results unveil the robust performance of the proposed approach based on the BA technique in the damping of the system’s vibrations.