In the present work, an experimental and numerical study has been performed to evaluate the suitability of the dielectric barrier discharge plasma actuators to reduce free vibrations of plates. Two configurations composed of two different plexiglass plates and identical actuators were manufactured. Experimental campaigns, in terms of laser doppler anemometer velocity measurements, flow visualization and proper orthogonal decomposition were carried out to characterize the plasma actuator and to validate the numerical models. The plasma-induced virtual body force for the numerical analysis has been calibrated based on the experimental body force and the induced flow field. Then numerical studies of the plasma effect on the flow around an oscillating plate was performed. An experimental modal analysis has been also performed to understand the vibration characteristics of the plate and to support the numerical study. A reduced-order model of the system, based on the harmonic oscillator, was developed to properly design an open loop controller (system natural frequency, amplitude and timing of the attenuation force). Eventually, the work demonstrates that the control strategy based on the plasma actuation is effective in reducing the plate vibrations. However, a deeper study and a more sophisticated control strategy would be required to significantly mitigate the flutter oscillations of airfoils in real applications.