## 3 Comparison of the Models  
In this section, three aforementioned models for EGW phenomena simulation in a multilayered composite are systematically compared. For this purpose, the same 8-layered symmetric laminate \([0^{\circ},90^{\circ}]_{2\text{s}}\) as described in Section 2.1.2 is considered. Owing to its symmetry properties, it is reduced to two plane-strain problems along planes \(x_{1}0x_{3}\) and \(x_{2}0x_{3}\) resulting in \([0^{\circ},90^{\circ}]_{2\text{s}}\) and \([90^{\circ},0^{\circ}]_{2\text{s}}\) laminates, respectively. The elastic constants of anisotropic plies as well as of corresponding homogenized layers which are required for plane-strain simulations [50] with respect to their orientation are summarized in Table 2. The material properties for PWTs that are employed for EGW excitation and sensing, as well as for the T-shaped stringer adhesively attached to the waveguide are provided in Tables 3 and 4, respectively. to predict adequately the behavior of fundamental and high-order antisymmetric waves in a multilayered waveguide including the values of their cut-off frequencies. The particular benefit of LWHM-model here is that for \(A0\) mode the dispersion curve evaluated with it is closer to the results of the complete multi-layered model than the one obtained with the SLWH-model. For symmetric modes, good coincidence between multi-layered and homogenized models is observed only for \(S0\) mode and for the frequency range where it is almost non-dispersive, i.e., up to \(f=400\) kHz. With the increasing frequency, not only the particular trajectories of \(s_{n}(f)\) for symmetric modes become dissimilar but the values of cut-off frequencies are also not properly addressed (e.g., for \(S2\) mode). For \([90^{\circ},0^{\circ}]_{28}\) waveguide, the obtained results are somewhat different. In general, the discrepancies between multilayered and homogenized models have increased. Although LWHM-model for \(A0\) mode in the frequency range below \(500\) kHz outperforms the SLWH one, for higher frequencies, on the contrary, SLWH \(s_{A0}(f)\) curve is closer to results evaluated with the multilayered model. Moreover, the values of cut-off frequencies for \(A1\) and \(A2\) modes predicted with SLWH deviate stronger from original data than those obtained with SLWH-model. It is interesting to note that for the frequency range when \(S0\) mode becomes dispersive, the LWHM-curve is notably closer to the results of the multilayered model. Figure 4: Slowness \(s_{n}(f)\) for \([0^{\circ},90^{\circ}]_{28}\): multi-layered waveguide (thick solid lines), homogenized waveguides (dashed and thin solid lines). Some of the aforementioned observations could be explained by comparing corresponding normal mode eigenforms. Figures 6-9 demonstrate eigenforms (energy flow \(e_{1}\) along the horizontal coordinate axis, vertical and horizontal displacements \(u_{k}\)) calculated via the multi-layered and SLWH models. Here normalized values \(\bar{u}_{k}(x_{3})\) and \(\bar{e}_{1}(x_{3})\) for each frequency are shown, where \(\bar{u}_{k}(x_{3})\) is normalized for each frequency by the maximum value of the displacement vector at frequency \(f\) over the waveguide \(\max\limits_{x_{3}}|\mathbf{u}(x_{3})|\) and \(e_{1}(x_{3})\) is normalized by the value \(\max\limits_{x_{3}}|\mathbf{e}_{1}(x_{3})|\). The time-averaged power density vector \(\mathbf{e}(\mathbf{x})\) or Umov-Poynting vector is evaluated as follows:  
\[e_{j}=\frac{\omega}{2}\operatorname{Im}\bigl{(}\sigma_{1j}\mu_{1}^{*}+\sigma _{3j}\mu_{3}^{*}\bigr{)}.\]  
The eigenforms calculated employing two approaches for two fundamental and two first higher-order modes have been analyzed. Similarly to the results presented in Figures 4 and 5, the analysis reveals good agreement between models at lower frequencies for \(A0\) and \(S0\) modes, whereas the discrepancy increases with the frequency growth for both orientations. A closer look at Figures 8 and 9 could explain the results regarding dispersion curves of high-order \(A1\) and \(S1\) modes.