Second-Order Model Reconstruction for Viscously Damped Substructures with Statically Determinate Interface

For single-point constrained and nonproportionally damped substructures, a data-driven method is proposed to reconstruct an underdetermined second-order model based on frequency response data at the statically determinate interface. By structured rational fitting of the interface acceleration impedance and applying a coordinate transformation to its state-space realization, the method yields a symmetric model that facilitates subsequent dynamic analysis. The main theoretical contribution is the inverse construction of a complex modal matrix that admits both the fitted interface impedance and the structural condition for model symmetry, with its general expression derived, and thereby enables an algorithm to seek mass positive definiteness. Numerical case studies on a lumped-parameter system and a solar array finite element model are performed to verify the method. The results demonstrate that the reconstructed models achieve high accuracy, which can serve as a reduced-order surrogate model for modal synthesis of spacecraft assembly.