Localized Effects of Piezopolymer Devices on the Dynamics of Inflatable Space-Based Structures

Inflatable space-based devices have become popular over the past three decades, as they offer minimized launch-mass and launch-volume. Since some satellites have mirror sections over fifty feet in diameter and struts with lengths over ninety feet, inflation while in orbit has become a necessary procedure. Once inflated, these space structures are subject to two types of vibrations: those induced mechanically by guidance systems and space debris and those induced thermally from variable amounts of direct sunlight as they orbit about earth. Controlling vibrations of spaced-based structures is critical to ensuring optimal performance.
The focus of this research is derived from an Air Force program to develop and model an active control system using smart materials to suppress the vibrations of inflatable communication satellites. When small piezoceramic devices are attached to an aluminum or steel structure, the effects of the piezo on the dynamic properties of the host are typically ignored. However, the inflatable satellites of interest to this project are manufactured from Kapton®, a thin, light polyimide film. Therefore, even a piezopolymer film actuator, such as PVDF, could greatly change the mass and stiffness values in the area under and around the patch, altering the dynamic behavior of the satellite.

Thin-walled pressure vessel theory was employed to assess the state of stress at any location on an inflated torus. A flat, rectangular coupon was selected at a general point on the structure and modeled as a membrane. The equation of motion for this membrane with clamped edges was derived and a closed-form solution for the natural frequencies and mode shapes was presented. The Rayleigh-Ritz and finite element methods were then seen to numerically approximate the natural frequencies and mode shapes for the bare membrane with a high degree of accuracy. A passive PVDF patch was then attached to the base membrane and the equation of motion derived using an energy approach. Since a closed-form solution was not readily available, the Rayleigh-Ritz and finite element methods were again employed to obtain approximate results that agreed remarkably well. Trends in natural frequencies for various patch areas and thicknesses were explored. It was shown, that membrane theory represented the added mass of the patch but was unable to account for the added stiffness of the PVDF attachment. Traditional membrane theory was also unable to model an active PVDF patch as a sensor for out of plane vibrations, but the ability of the patch to alter the tension in the base layer was predicted.