Nonlinear Approaches in Engineering Applications pp 237-263 | Cite as

# Nonlinear Deployable Mesh Reflectors

Design, Modeling and Analysis

Chapter

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## Abstract

A reflector is a structural device that receives and reflects electromagnetic signals. A reflector normally has a dish shape as working surface and is supported by another structure (commonly a truss) behind. Unlike reflectors on the ground, when a reflector is installed onto a satellite or a space shuttle and used in space, many crucial requirements must be considered, one of which requires that the reflector has to be deployable. Because the size of a space reflector is usually much larger than the spacecraft that carries it, the reflector must be first folded into a small volume on the ground that can be stored inside the spacecraft, and then be deployed into the space after the spacecraft has been launched onto the designated orbit. After the deployment is completed, the reflector will produce and automatically maintain a working surface (aperture) with tolerant surface errors. Due to this particular feature, such structural devices are called deployable reflectors. As one of many types of deployable reflectors, deployable mesh reflectors have broad space applications, and have brought continuously interest in academia and industry in the past. Deployable mesh reflectors have been used in several renowned projects, such as ETS VIII for satellite communication, MBSAT for global broadcasting, “NEXRAD in Space (NIS)” mission for remote sensing and climate forecasting and GEO-mobile satellites by Boeing for mobile communications (Thomson 2002; Natori et al. 1993; Meguro et al. 1999; Im et al. 2003). Deployable mesh reflectors are also envisioned for many other applications such as high data rate deep space communications, Earth and planetary radars, and RF astronomy observations. Figure 8.1 illustrates a structure design for deployable mesh reflectors that has been considered by NASA engineers and studied in our research. The reflector is supported by the flat truss on the boundary and the working surface is constructed by the mesh and the front net. The nodes of the front net and rear net are connected by tension ties, where the actuators are installed. Those actuators properly adjust the length of the tension ties, so as to generate and maintain the desired working surface during the deployment and the in-space mission. According to the structural configuration in Fig. 8.1, the mesh reflector can be modeled as a nonlinear truss structure (shown in Fig. 8.2), whose elements can only sustain axial tension stress. The structure is fixed on the boundary and the working surface is formed by the truss elements. The tension ties are connected to the nodes, which provide the vertical external loads because of the symmetry between the front net and the rear net in the configuration under the concern. There are two crucial factors in performance assessment of deployable mesh reflectors: the aperture size of the reflector (mostly in term of the diameter) and the root-mean-square (RMS) value of the surface error. According to the antenna theory, larger-sized reflectors are capable of transmitting greater amount of data with higher resolution, and the smaller surface RMS error implies broader frequency bandwidth of the transmitted signals. The characteristic ratio, which is defined as the ratio of the reflector diameter to surface RMS error, is one of the key parameters to evaluate the performance of the mesh surface. Obviously, to increase the characteristic ratio, we can either increase the diameter of the reflector or decrease the surface RMS error; both of which, however, will enlarge the number of mesh cells, and increase the complexity and difficulty in design and manufacturing of this kind of reflectors. Therefore, development of large-sized deployable reflectors with small surface RMS errors, although in urgent demand due to the stringent requirements on surface performance to serve signal with high accuracy, has been a challenge for years.Previous investigations (Hedgepeth 1982a,b) have shown the performance limitation due to thermoelastic strain and manufacturing errors of materials in passive structure. It has been suggested that active surface (shape) control becomes necessary to improve the surface performance of deployable space reflectors for space missions and other applications. In this chapter, we present the results from our research project on developing the active surface control (ASC) architecture by using nonlinear modeling and analysis techniques.The remaining of the chapter is arranged as follows: Sect. 8.1 specifically states the objectives of the research. Section 8.2 presents the theoretical formulation of problem modeling and analysis. Then the numerical results and discussions will be provided on a sampled deployable mesh reflector in Sect. 8.3. Finally, Sect. 8.4 addresses some remarks on the progress of development of ASC architecture and the future research direction, and then concludes the chapter.

## Keywords

External Load Trust Region Quadratic Programming Problem Surface Error Truss Structure
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Notes

### Acknowledgements

This work was a result of the authors’ previous projects partially sponsored by NASA’s Jet Propulsion Laboratory.

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