Strain-Based Dynamic Force Reconstruction Using Frequency-Domain Inversion

This study presents a strain-based methodology for reconstructing dynamic forces acting on a structure using strain, strain rate, and strain acceleration measurements. Unlike conventional methods that require inversion of the structural response matrix, this approach reformulates the equation of motion in terms of strain-based quantities and parameterizes it using structural matrices.These matrices are computed using a least-squares formulation from frequency-domain calibration data, avoiding direct inversion and enhancing numerical stability. The method is implemented on a finite element model of a cantilever beam subjected to sinusoidal excitation. Results show accurate force reconstruction for a broad range of excitation frequencies. The approach is further validated under noisy conditions using frequency-domain filtering, demonstrating robustness to measurement noise. The results highlight the importance of sensor placement and the selection of calibration frequency.