Noise and vibration are common issues that may have a negative impact on human’s’ health. To minimize their consequences, several vibroacoustical methods may be employed. One well-known method is Piezoelectric Shunt Damping (PSD). Over the years, many approaches have been investigated, from passive, state switching circuits to active pulse-switching. In this paper, the authors propose three PSD implementations—passive Synchronized Switch Damping on Inductor (SSDI), semi-active SSDI and active Synchronized Switch Damping on Voltage source (SSDV)—for a single-panel structure mounted on a rigid-frame casing. The nine Macro Fiber Composite (MFC) elements were mounted on the plate based on preliminary simulations in FreeFEM. Then, the theoretical results were validated by an identification experiment. The main research is concentrated on the Sound Pressure Level (SPL) and structural vibrations reduction for selected frequencies. The active method provided the highest reduction of vibration—up to 5.5 dB for maximal possible loudspeaker level without overdrive and up to 7.5 dB for lower excitation levels.