A hierarchical mapping framework for dynamic response of a wing-shaped structure

A novel hierarchical substructuring formulation is proposed to consistently capture dynamic responses from globally coarse models to locally refined substructures. Starting from an available global coarse model, the proposed formulation hierarchically enriches local substructures to recover fine-scale physical information and dynamic fidelity. Within this framework, dynamic equilibrium and kinematic compatibility are rigorously preserved across hierarchical levels, enabling analytical recovery of local dynamic behaviors from global representations. The proposed theory establishes a unified foundation for bridging global and local dynamic models, and extends the classical substructuring methodology toward a multi-level dynamic enrichment paradigm. The formulation is applied to a wing structure to assess its applicability. Numerical evaluations demonstrate that the hierarchical substructure model successfully reconstructs the local modal characteristics of the fully refined finite element model, thereby validating the theoretical consistency and effectiveness of the proposed approach in supporting analyses across multiple fidelity levels and design stages. This framework provides a general pathway for hierarchical dynamic modeling and multiscale analysis of complex aerospace structures.