The control of noise and vibrations using conventional damping materials is typically associated to mass penalties in a vehicle. A lightweight alternative employs piezoceramic materials connected in series to a resistor and an inductor (R-L circuit) to perform as mechanical vibration absorber, called piezoelectric resonator. In this paper, piezoelectric resonators are designed to attenuate vibration in a vehicle panel. The choice of design parameters, such as correct placement for the piezoelectric patches and the optimal electrical circuit values, is assisted by Finite Element simulation (FE) and theoretical analysis. Measurements of Sound Transmission Loss (STL) and modal analyses are conducted to demonstrate the efficiency of the proposed technique when compared to a conventional damping material.