Inverse finite element methodology for high-resolution mode shape reconstruction of plates and shells under random excitation

This study introduces a novel implementation of the inverse finite element method (iFEM) for full-field mode shape reconstruction of plate and shell structures under random vibration. The proposed methodology, termed iFEM-MoRe (Mode Reconstruction), seamlessly integrates classical iFEM with Fourier transformation using Welch’s estimation method. By processing dynamic strain measurements, iFEM-MoRe extracts the frequency spectrum of displacements across the structure, enabling accurate identification of natural frequencies and high-fidelity reconstruction of full-field mode shapes. Designed for both 2D and 3D complex structural topologies, iFEM-MoRe operates without prior knowledge of the excitation, making it a powerful and adaptable tool for structural health monitoring in real-world operational environments. The high accuracy of iFEM-MoRe is validated through experimental and numerical studies. In the experimental analysis, shape reconstruction and mode identification are performed on a wing-shaped composite plate using discrete strain data from surface-mounted sensors. Numerically, the dynamic response of the same wing under random vibration is analyzed, demonstrating the method’s reliability. A rectangular plate subjected to random vibration is also investigated, where iFEM-MoRe results show excellent agreement with finite element modal analysis. Finally, the framework’s capability for a complex geometry is validated through the analysis of a curved plate under random vibration, with results compared to forward modal solutions. These comprehensive studies confirm that iFEM-MoRe delivers accurate mode identification and reconstruction, establishing its robustness and versatility for full-field dynamic analysis of challenging structural cases under random vibration.