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