Minimal mass (ultra lightweight) and high packaging efficiency (stowage volume) are the most important factors associated with space technology and hence they become more attractive traits for getting larger bandwidth satellites on-orbit. Nowadays, maintaining the surface shape of pre-tension membranes to instrument precision has become a more challenging problem. Hence, membrane reflectors are receiving increasing attention for mission architectures that need extremely large in-space deployable antennas. This paper presents the finite-element investigation of a rectangular, flat thin membrane using polyvinylidene fluoride (PVDF) piezo-actuated material as an actuator/sensor. The passive effect of PVDF on the dynamics of an inflatable space-based rectangular shaped structure has been studied and trends in natural frequencies for various patch areas and thickness have been explored. Investigation shows that rather than using the various numbers of patches to the practical system for controlling their vibration behavior, the single patch with the appropriate thickness can easily control the desired vibration behavior. It can therefore be concluded that the discrete sensor/actuators devices are to be preferred to realize lower weight and effective control authority for the modest values of actuator voltages for active vibration control of practical structures.