This paper presents a simulation study concerning the low and mid frequencies control of flexural vibration in a lightly damped thin plate equipped with five time-varying shunted piezoelectric patch absorbers. The panel is excited by a rain-on-the-roof broad frequency band stationary disturbance. The absorbers are composed by piezoelectric patches connected to time-varying RL shunt circuits. Discrete or continuous variations over time of the shunts are implemented in such a way as to either switch, between given values, or sweep, within certain ranges, the natural frequency and damping factor of the electro-mechanical absorbers to control either the resonant response of targeted flexural modes of the plate with natural frequency comprised between 30 Hz and 1 kHz or to control the resonant responses of all flexural modes with natural frequencies comprised between 30 Hz and 1 kHz. The proposed system is firstly presented; then, the vibration control effects produced by a single patch and by the array of five patches implementing the switching and sweeping shunts are investigated. Both time-varying operation modes produce significant vibration control effects, with reductions of the resonance peaks of the target resonances or target frequency band up to 12 dB. The piezoelectric patch absorbers with sweeping shunts offer an interesting practical solution since they are operated blindly, thus they do not require a system identification during installation and effectively work without on line tuning also on systems whose response may vary substantially in time.