## 1 Introduction  
Reflector antennas have been applied to satellite communication, remote sensing, and radio astronomy for decades [1; 2; 3; 4]. Radio astronomy detection is mainly carried out with single-aperture radio telescopes or interference array antennas. The antenna array can be composed of various antennas such as parabolic cylindrical reflector antennas, parabolic reflector antennas, and dipole oscillator arrays. Among these antennas, the large parabolic cylindrical reflector antenna is favored by more and more researchers due to its unique advantages such as high gain, strong directivity, and multiple feeds [5]. Since the 1950s, many countries have built a number of typical cylindrical reflector antennas in succession, such as the Ooty Radio Telescope [6], the Molonglo Observatory Synthesis Telescope of Australia [7], and the Nagoya IPS Stations of Japan [8]. China has also proposed a specific experimental prototype of the parabolic cylindrical reflector antennas in the Tianali Project [9]. Some scholars have carried out the structural design and mechanical analysis of these parabolic cylindrical reflector antennas [10]. In 2015, China built an antenna array for dark energy detection that consisted of three 45 \(\times\) 15 m parabolic cylindrical reflector antennas and sixteen parabolic reflector antennas [11]. All of these illustrate that there are broad development and application prospects for parabolic cylindrical reflector antennas. Parabolic cylindrical reflector antennas can be divided into fixed antennas and movable antennas according to different observation objects [12]. The feed of the movable antenna is fixed to the reflector surface through brackets. Then, the reflector surface is mounted on the pitch axis through the back frame structure. Generally, the weight of an antenna is roughly proportional to the square of the aperture for movable antennas [13]. In comparison with the fixed antenna, the movable reflector antenna can observe more signal sources and track a single signal source for a longer time. With increasing demands of observation, the aperture of the antenna becomes larger, which is followed by some challenges in mechanical rotation [14; 15; 16], feed support [17], and structural weight [18]. Furthermore, excessive weight brings great challenges regarding the construction process and production cost. It also causes a negative impact on the service life of reflector antennas. For example, since the start of its observations in 2001, the azimuth track of the Green Bank Telescope (GBT) has presented a series of problems due to its heavy weight and insufficient design, including tangential slippage of the base and wear plates, excessive tilting of the azimuth wheels, surface deterioration between the wear and base plates, fatigue fracture of bolts, cracks in wear plates, and so on [19; 20; 21]. Based on the background above, it has been stated that the huge weight of a large-aperture reflector is a critical challenge to the mechanical mechanism of movable antennas, which appeals to numerous scholars. Some scholars have committed to developing the design of mechanical systems and actively adjusting the reflector surface to improve the working performance [22; 23; 24]. Alternatively, some scholars have proposed some optimization ideas to reduce the weight and construction cost of reflector structures [25; 26; 27]. Most studies regard the movable reflector antenna on the ground. The gravity of the superstructure is concentrated on the azimuth mechanism, resulting in the range of problems mentioned above. In contrast, the movable reflector antenna set on the water surface can effectively resist the influence of gravity through buoyancy. Nevertheless, to the authors' knowledge, there are few studies on this [28]. Hence, a floating cylindrical reflector antenna (FCRA) is put forward in this study based on the current research. The buoyancy of water can resist the gravity of the structure.