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The use of time reversal methods for localization and characterization of damages in plates is usually combined with high frequency guided waves in a local elastic wave propagation formulation. In such a situation, pulses and echos may be clearly separated in time. As a consequence, the diffracted field on a damage with large geometrical dimensions compared to the wavelength used for wave propagation allows to consider the structure itself as "near infinite" because the modal behavior is not apparent. However, those high requencies may not be required and in the presented approach, medium frequencies are used and boundary conditions need to be considered. The interest of this frequency range is in using lightweight signal processing devices limited to low data transfer rates as expected for in flight fuselage skin inspections. It also allows to filter artifacts like very small damages in the structure. This study focuses on the case of wavelengths which are in the order of the largest geometrical dimension of the cracks. In the paper, a modelling tool is first extended to describe the vibration behavior of pristine and damaged finite thin plates in the low and medium frequency range below 50 kHz. The proposed analytical model employs a Hierarchical Trigonometric Functions Set (HTFS) to characterize homogeneous plates with through cracks. To approximate the effect of a small crack in a plate for all combinations of classical boundary conditions, high order approximation functions are required. The proposed approach takes the advantage of the stability of the HTFS for these high orders. A notable advantage of this model is that it does not require a dense uniform meshing of the plate, with a minimum of 10 nodes per wavelength, as most finite element models require. The time reversal concept introduced before is thus validated with this model for a finite plate with known boundary conditions. Experimental validation of the model is conducted in the time domain for pristine and cracked plate structures and shows great potential for crack detection.
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