Dynamic modeling and vibrations of large deployable mesh reflectors

Large deployable mesh reflectors play a critical role in satellite communications, Earth observation, and deep-space exploration, offering high-gain antenna performance through precisely shaped reflective surfaces. Traditional dynamic modeling approaches—such as wave-based and finite element methods—often struggle to accurately capture the complex behavior of three-dimensional reflectors due to oversimplifications of cable members. To address these challenges, this paper proposes a novel spatial discretization framework that systematically decomposes cable member displacements into boundary-induced and internal components in a global Cartesian coordinate system. The framework derives a system of ordinary differential equations for each cable member by enforcing the Lagrange's equations, capturing both longitudinal and transverse internal displacement of the cable member. Numerical simulations of a two-dimensional cable-network structure and a center-feed parabolic deployable mesh reflector with 101 nodes illustrate the improved accuracy of the proposed method in predicting vibration characteristics across a broad frequency range. Compared to standard finite element analysis, the proposed method more effectively identifies both low- and high-frequency modes and offers robust convergence and accurate prediction for both frequency and transient responses of the structure. This enhanced predictive capability underscores the significance of incorporating internal cable member displacements for reliable dynamic modeling of large deployable mesh reflectors, ultimately informing better design, control, and on-orbit performance of future space-based reflector systems.