A data-driven approach for cross-sectional deformation mode identification and higher-order dynamic modeling of thin-walled beams

This paper presents a data-driven framework for identifying cross-sectional deformation modes and establishing a corresponding one-dimensional higher-order dynamic model for thin-walled beams. Using the free-vibration results of a shell model as the data source, nodal displacements are extracted and preprocessed to construct a deformation dataset. The approach employs principal component analysis (PCA) to extract dominant cross-sectional deformation modes, thereby reducing reliance on empirical assumptions while preserving physical interpretability. The identified deformation patterns are further converted into explicit shape functions through polynomial fitting, and the most representative modes are selected to construct a one-dimensional higher-order model with reduced degrees of freedom. In this way, the proposed model captures both classical and higher-order deformations without manually prescribed analytical higher-order mode shapes; piecewise polynomials serve only as a general reconstruction space, while the higher-order cross-sectional modes are identified from vibration data. Numerical results show that the maximum frequency error is 3.84% for the benchmark beam and remains below 5% for the examined geometric variations and I-section beam, while the representative stress errors are also below 5%. Without repeating PCA, the maximum frequency error increases to 7.72% under the clamped–clamped boundary condition, whereas the global degrees of freedom remain 88.54% lower than those of the shell element model. Overall, the proposed method improves the description of complex cross-sectional deformations while retaining the computational efficiency of a one-dimensional model.