## 4 Discussion  
The configuration and optimization of guided wave-based NDT/SHM systems is still a challenging task that requires extensive and time-consuming numerical simulations, especially when complex wave phenomena in composite structures incorporating constructive irregularities and/or defects as well as a set of installed sensors are considered, e.g., see Ref. [19]. Therefore, it is a natural temptation to replace complex multi-layered laminates with an effective single layer in order to cut down computational costs in the numerics. The application of such an approach for EGW phenomena simulations might be particularly beneficial when standard FEM codes are employed, since no specific modification to the FEM-based evaluations are required. The results presented in the current paper demonstrate, however, that the researchers should be careful when applying such effective models for simulating guided waves propagation and scattering in anisotropic multi-layered composites with PMTs and inhomogeneities. Within this study, two approaches for the evaluation of the elastic properties of such effective single layer are implemented, namely, SLWH and LWHM models. In the first one, the corresponding stiffness matrix \(\tilde{C}_{ij}\) is directly related to the sublayers' elastic properties through the Equation (6). However, this approach does not take into account the peculiarities of the composite stacking sequence, i.e., identical matrices \(\tilde{C}_{ij}\) would be obtained either for symmetric or non-symmetric balanced cross-ply laminates with  
Figure 16: Voltage \(\phi(f)\) measured at the sensor on the surface of the multi-layered waveguide \([0^{\circ},90^{\circ}]_{28}\) (thick solid line), and waveguides with effective properties estimated according to the SLWH-model (thin solid line) and the LWHM-model (dash-dotted line) in the case of the surface-mounted stringer. Figure 15: Voltage \(\phi(f)\) measured at the sensor on the surface of the multi-layered waveguide \([90^{\circ},0^{\circ}]_{28}\) (thick solid line), and waveguides with effective properties estimated according to the SLWH-model (thin solid line) and the LWHM-model (dash-dotted line) in the case of the surface-mounted stringer. and \(\bar{C}_{44}=\bar{C}_{55}\). Since these equalities hold, the SLWH model is not capable of tackling the difference between EGW dispersion properties for \(0^{\circ}\) and \(90^{\circ}\) propagation directions typical for symmetric cross-ply composites [51]. In the proposed LWHM approach, this issue is addressed by evaluating \(\bar{C}_{ij}\) through the optimization problem where angular dependencies of EGW dispersion curves solve as an input. However, their preliminary calculation is required and the solution of the corresponding minimization problem (7) should be performed. With the provided numerical results, it is illustrated that effective single layer models cannot exactly predict the dynamic behavior of symmetric cross-ply laminates fabricated from unidirectional prepregs. Even for the fundamental \(A0\) mode, its dispersion properties evaluated within SLWH and LWHM models and multi-layered model differ for the orientation \(90^{\circ}\) related to the plane-strain problem for \([90^{\circ},0^{\circ}]_{28}\) sample. If the pair of PWTs, i.e., actuator/sensor, mounted on the surface of an 8-layered symmetric laminate is considered, both effective models give results that are qualitatively similar to the multi-layered model only at low frequencies (approximately up to 150-200 kHz). The discrepancy becomes larger and the frequency range, where the effective models are valid, decreases if the T-shaped stringer is glued on the surface of the laminated structure.