*4.2. Dispersion Curves*

Figures 9 and 10 present the 2-D view of the wavenumber–frequency information, which was obtained by carrying out the 2D-FFT (see Equation (8)) of the time series registered for four different excitation frequencies in equally spaced points on the plate surface. The final map presents the dispersion curves representing antisymmetric Lamb wave modes described by Equation (2). Based on the 2D-FFT results, the shape of the curve for the first antisymmetric mode was reconstructed. For comparison, the wavenumber–frequency information obtained for the homogeneous concrete model is presented in Figure 9, while Figure 10 contains the results for nine heterogeneous models.

As we can see, the aggregate ratio clearly influences the visibility of the particular dispersion curves. In the case of the homogeneous material, the curves can be unambiguously distinguished. The presence of aggregate particles and aggregate-wave interactions affecting the signals' characteristics resulted in deterioration of the quality of the maps. The map with the worst quality was obtained for model C3 characterized by the highest aggregate ratio and the largest particles (see Table 2). Heterogeneity hinders the reconstruction of dispersion curves based on wavenumber–frequency information.

−

(, )

max ( )

ˆ (, )

**Figure 9.** Wavenumber–frequency representation for homogeneous concrete model.

*ρ*

**Figure 10.** Wavenumber–frequency maps determined for numerical models of heterogeneous concrete plates: (**a**) group A; (**b**) group B and (**c**) group C.

1 1

1 1 

 
