A new class of smart foams is introduced to simultaneously control the vibration and noise radiation from flexible plates coupled with acoustic cavities. The proposed smart foam consists of passive foam/piezoelectric composite layers. The proposed smart foam can simultaneously control structural and acoustic cavity modes over a broad frequency range. A comprehensive theoretical study of the smart foam elements is introduced, in order to optimize the design and performance of this hybrid actuator. A finite element model is developed to study the interactions among the smart foam components and with an acoustic cavity. The developed finite element model is a reduced 2D model, which was compared with the original 3D model where it managed to capture all the targeted dynamic characteristics. The developed theoretical and experimental techniques will provide invaluable tools for the design and application of the proposed smart foam to a wide variety of systems such as passenger cars, helicopter, aircraft cabins and other flexible enclosures, where their operation as quiet platforms is critical to the success of their mission.