Finite Element Modeling and Active Control of an Inflated Torus Using Piezoelectric Devices
Satellite antenna design requirements are driving the satellite size to proportions that cannot be launched into space using current technology. In order to reduce the launch size and mass of satellites, inflatable structures, also known as gossamer structures, are being considered. Inflatable space-based structures are susceptible to vibration disturbance due to their low stiffness and damping. This thesis discusses the structural dynamics and vibration suppression via piezoelectric actuators, using active control of an inflatable torus.
A commercial finite element package, ANSYS, is used to model the inflated torus. The effect of torus aspect ratio and inflation pressure on the vibratory response of the structure is investigated. The interaction with the torus of the surface-mounted piezoelectric patches, made of PVDF, is modeled using Euler-Bernoulli beam theory. A state space representation is created of the model in modal space and modal truncation is performed. Traditional control tools are used to suppress vibration in the structure. First observer-based full state feedback is used, then direct output velocity feedback is explored.
The aspect ratio of the torus is found to significantly influence the mode shapes. Toroids of small aspect ratios, skinny toroids, act like rings, but the mode shapes of toroids with large aspect ratios are much more complicated. For toroids of small aspect ratios, increasing the inflation pressure simply results in stiffening the ring, thereby increasing the natural frequencies. Increasing the pressure in toroids with large aspect ratios changes both the mode shapes and natural frequencies. The passive effect of PVDF on the dynamics of the torus is small, the mode shapes do not change and the frequencies are only slightly reduced. Active control of toroids with small aspect ratios using piezoelectric devices is effective. It may be more difficult to control toroids with large aspect ratios because the mode shapes are much more complicated than the simple ring modes found in toroids with small aspect ratios.