In this study, a new modal-based structural health monitoring (SHM) approach is proposed based on the inverse finite-element method (iFEM) to perform damage diagnosis of the plate and shell structures based on full-field modal parameters reconstructed from discrete sensor data. The iFEM formulation can effectively solve a shape sensing or deformation reconstruction problem, where changing displacements of the structure are predicted by minimizing a variational least squares error function of analytical and experimental discrete strains with respect to unknown displacements. Such a solution provides the time-domain response of the structures, which may be solely not enough to extract the dynamical properties of the structure for underlying the unhealthy conditions. To address this important gap, the iFEM is enhanced by processing the full-field displacement solution with fast Fourier transformation, enabling mechanical parameters to switch from time to frequency domain. This posterior step, named iFEM Modal Reconstruction (iFEM-MoRe), can recover full-field dynamical characteristics from the response discrete Fourier transformation of a structure for the investigation of unhealthy structural conditions and damage identification. In this regard, iFEM-MoRe allows the utilization of the entire time/frequency-domain response of structures for correlating modal/dynamical characteristics with structural anomalies. To verify the capability of the approach, intact and damaged cases of benchmark problems are solved. According to the results, it is demonstrated that iFEM-MoRe can predict highly precise natural frequencies just from discrete sensor data without loading/material information. Also, it is revealed that iFEM-MoRe can highly accurately reconstruct full-field mode shapes and diagnose damaged conditions by pinpointing alternated dynamical characteristics of structures as compared to intact parameters. Overall, the presented approach can serve as a complementary toolbox for vibration and/or statistical time series SHM methods to understand full-field modal characteristics of damaged cases just from a network of sensors.
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