Dynamic Response Of A Satellite With Flexible Appendages And Its Passive Control
Joseph, Thomas K
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Most present day spacecrafts have large interconnected solar panels. The dynamic behavior of the spacecraft in orbit can be modeled as a free rigid mass with flexible elements attached to it. The natural frequencies of such spacecrafts with deployed solar panels are very low. The low values of the natural frequencies pose difficulties for maneuvering the spacecraft. The control torque required to maneuver the spacecraft is influenced by the flexibility of the solar arrays. The control torque sets up transient oscillations in the flexible solar panels which in turn induces disturbances in the rigid satellite body and the payload within. Therefore the payload operations can be carried out only after the disturbances die out. For any reduction of the above disturbances it is necessary to understand the dynamic behavior of such systems to an applied torque. The present work first studies the nature of the disturbances. The influence of structural parameters on these disturbances is then investigated. Finally, the use of passive damping treatment using viscoelastic material is investigated for the reduction of the disturbances. In order to understand the nature of vibrations induced in the flexible appendages of a satellite during maneuvers, we model the maneuver loads in terms of applied angular acceleration as well as varying torque. The transient decay of the disturbance of the rigid element is characterized by the dynamic characteristics of the flexible panels or appendages. It is shown that by changing the stiffness of the panel the response of the rigid element can be modified. A simple model consisting of an Euler-Bernoulli beam attached to a free mass is next considered. The influence of various parameters of the EulerBernoulli beam in mitigating vibration and thereby the disturbance in the rigid mass is investigated. As the response of the rigid system mounted with the large flexible panels are influenced by the dynamics of the flexible panels, reduction of these disturbances can be achieved by reducing the vibration in the flexible panels. Therefore application of viscoelastic materials for passive damping treatment is investigated. The loss factor of a structure is significantly improved by using constrained viscoelastic layer damping treatment. However providing a constrained layer damping treatment on the entire structure is very inefficient in terms of the additional mass involved. Therefore damping material is applied at suitable optimal locations. In previous studies reported in literature, modal strain energy distribution in the viscoelastic material as well as the base structure is used as a tool to arrive at the optimum location for the damping treatment. It is shown in this study that such locations selected are not the optimum. A new approach is proposed in this study by which both the above shortcomings are overcome. It is shown that use of a parameter that is the ratio of the strain in the viscoelastic material to the angle of flexure is a more reliable measure in arriving at optimal locations for the application of constrained viscoelastic layers. The method considers the deformations in the viscoelastic material and it is shown that significant values of loss factors are achieved by providing material in a small region alone. We also show that loss factor can be improved by providing damping material near the interface region. The loss factor can be further improved by incorporating spacers by using spacer material having higher extensional modulus. Also shown is the fact that loss factor is unaffected by the shear modulus of the spacer material. Experiments have been conducted to validate these results. In a related study we consider honeycomb type flexible structures since in most of the spacecraft applications honeycomb sandwich constructions are employed. But loss factors of sandwich panels with constrained layer damping treatment are seldom discussed in the literature. Use of viscoelastic layers to improve the loss factors of the honeycomb sandwich beams is explored. The results show that the loss factors are enhanced by increasing the inplane stiffness of the constraining layer. These conclusions too are validated by experimental results. Finally a typical satellite with flexible solar panels is considered, and the use of the viscoelastic material for improving the damping is demonstrated.