Purpose <p>The time-varying lateral vibration of the radial ribs induced by the deployment movement of the satellite antenna has adverse effects on its surface accuracy and fatigue life. This paper utilizes the method of a hollow component of the radial ribs containing multi-petal friction dampers (MPFD) with high energy dissipation and a wide frequency band to achieve lateral time-varying vibration control of the satellite antenna.</p> Methods <p>Firstly, the dynamic model of the loss factor of the oscillation system is developed, which takes advantage of friction loss energy of nonlinear structure damping. After establishment of the lateral dynamic model of the component installed with the MPFD, the effects of the thickness and the number of petals on the optimal designparameters of the MPFD are analyzed based on the optimization algorithm. Subsequently, the transfer matrixmethod is used to establish a dynamic sub-scale model of the component of the radial ribs. The comparativedamping validation experiments are performed to measure the loss factor of the lateral oscillation system subjectedto dynamic excitation. Finally, the simulations investigate the multiple resonance response of the radial ribs installedwith optimally designed MPFDs to demonstrate the effectiveness of suppressing the time-varying lateral vibrationafter and during the antenna deployment.</p> Conclusion <p>Theoretical studies and experimental results show that the proposed design method of the MPFD has a significant effect on suppressing the lateral time-varying and multi-mode lateral vibration of the satellite antenna.</p>