Surface Accuracy Analysis and Mathematical Modeling of Deployable Large Aperture Elastic Antenna Reflectors Open Access
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A deployable antenna reflector consists of an inflatable elastic membrane that is supported about its perimeter by a set of elastic tendons and is subjected to a constant hydrostatic pressure. A design may not hold the desired parabolic shape due to an elastic deformation of the surface, particularly near the rim. We can compute the equilibrium configuration of the reflector system using an optimization--based solution procedure that calculates the total system energy and determines a configuration of minimum energy. Analysis of the equilibrium configuration reveals the behavior of the reflector shape under various loading conditions. The pressure, film strain energy, tendon strain energy, and gravitational energy are all considered in this analysis. The surface accuracy of the antenna reflector is measured by an RMS calculation while the reflector phase error component of the efficiency is determined by computing the power density at boresight. Our error computation methods are tailored for the faceted surface of our model and they are more accurate for this particular problem than the commonly applied Ruze Equation.Previous analytical work on parabolic antennas focused on axisymmetric geometries and loads. Symmetric equilibria are not assumed in our analysis. In addition, this dissertation contains two principle original findings: (1) the typical supporting tendon system tends to flatten a parabolic reflector near its edge. We find that surface accuracy can be significantly improved by fixing the edge of the inflated reflector to a rigid structure; (2) for large membranes assembled from flat sheets of thin material, we demonstrate that the surface accuracy of the resulting inflated membrane reflector can be improved by altering the cutting pattern of the flat components.Our findings demonstrate that the proper choice of design parameters can increase the performance of inflatable antennas, opening up new antenna applications where higher resolution and greater sensitivity are desired. These include space applications involving high data rates and high bandwidths, such as lunar surface wireless local networks and orbiting relay satellites. A light--weight inflatable antenna is also an ideal component in aerostat, airship and free balloon systems that supports communication, surveillance and remote sensing applications.
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