It is found that when the surface error is small the calculated gain loss is close to Ruze's results, but with increasing of the surface error, the Ruze prediction departs from our results. The maximum gains are compared with the results given by the Ruze formula. It can be seen that the maximum gain is rapidly decreased from 41.09 to 37.33 dB after only 1 day and slow changing after dozens of days. With the aid of ( 14), the time-dependent radiation pattern of reflector antenna at 20 GHz in the E-plane is calculated and some results are shown in Fig. (a) Cables’ tension variations, (b) Nodal displacements along the x-axis, (c) Nodal displacements along the y-axis, (d) Nodal displacements along the z-axis Time-dependent behaviours of the cable-net reflector In Section 4, some conclusions are summarised. In Section 3, the proposed method is applied to an axis-symmetric reflector antenna to confirm the practicability, validity and robustness of the proposed method. In Section 2, the formulation derivation process for the time-dependent radiation pattern is presented in details. Thus, this paper would like to investigate the influence of the time-dependent behaviour on antennas’ electrical performance. Therefore, previous work concentrated on the radiation pattern analysis of the distorted reflector antennas – ], but only time-independent surface errors are considered. However, the Ruze formula is proposed for small random errors but not systematic errors, and only the relationship between the gain loss and the RMS can be revealed. Traditionally, the root mean square (RMS) of the nodal displacements could be used to estimate the boresight gain loss of the antennas by the Ruze formula, ]. To authors’ knowledge, almost all existing literatures regarding the C&R behaviour of the cable-net reflector antennas are focused on the surface error distribution of the cable nets. Our previous work, ] regarded the viscoelastic behaviour of the cables as the adjustment of cables’ elongation rigidity, and established a C&R model for the cable-net reflectors based on Schapery's non-linear viscoelastic theory, and eventually calculated a time-dependent tangent stiffness matrix for the C&R behaviour analysis of the cable-net reflectors with the aid of the non-linear force density method. In the previously referenced papers, the creep constitutive equations were directly used for the adjustment of cable lengths.
Kmet and Mojdis, ] combined the viscoelastic constitutive theory with two shape-finding methods (dynamic relaxation method ] and force density method, ]) to obtain the time-dependent tangent stiffness matrix.
In recent years, there are some scholars trying to establish the time-dependent non-linear equations to describe the mechanical properties of the cable-net structures ]. (a) Hoop truss cable-net reflector composed of triangular net, (b) Umbrella cable-net reflector composed of quadrilateral nets This time-dependent characteristic is so-called C&R behaviour of cable-net reflector antennas which will eventually decrease the antenna's working accuracy. However, even if the cable net is in equilibrium at the initial stage, the equilibrium will change without any external loads in the next time. However, the load-elongation characteristics of these fibre materials are viscoelastic. In addition, the cable net is often constituted by fibre materials such as polyethylene, polyamide and aramid because of their excellent mechanical properties like lightweight, low coefficient of thermal expansion and high axial stiffness. As the support of the RF reflective mesh, the cable net is one of the most important components of the antenna to keep excellent electrical performance and long operating life. It can be seen that the cable-net reflectors are mainly composed of supporting truss, cable net and RF reflective mesh. 1 a and b are the most common used structure forms at present. One reason for this drawback is the creep and recovery (C&R) behaviour of cable-net reflectors. However, a significant drawback to these antennas is the limited surface accuracy of the reflectors, which has imposed a restriction on the ability to reflect RF communications at shorter wavelengths ]. As improvement in system capacity is required, cable-net reflector antennas are faced with increasing accuracy and size requirements for space missions.
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