## 3 Results and Discussion
### Case I: Numerical Simulation  
#### 3.1.1 Modelling of the Blade Using Finite Element Method  
The numerical simulation was carried out using the Finite Element Method procedure (FEM). In the FEM calculations of the rotor blade under investigation, the primary numerical model consisted  
\begin{table}
\begin{tabular}{c c} \hline \hline  & **Dimension [mm]** \\ \hline Total length & 1740 \\ Max width & 160 \\ Tip width & 32 \\ Measured length & 1440 \\ Thickness of spar & 2.0 \\ Thickness of Section 1 (near blade root) & 2.0 \\ Thickness of Section 2 (middle part of blade) & 1.5 \\ Thickness of Section 3 (near blade tip) & 1.0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geometrical features of the blade.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Epoxy Resin** & **Glass Fiber** \\ \hline Young modulus, E & 3.43 GPa & 66.5 GPa \\ Poisson ration, \(\
u\) & 0.35 & 0.23 \\ Kirchoff modulus, G & 1.27 GPa & 27 GPa \\ density, \(\rho\) & 1250 kg/m\({}^{3}\) & 2250 kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Properties of composite materials components.  
Figure 3: Scheme of the research object.  
of 5409 isoparametric shell elements. Each finite element had eight nodes and six degrees of freedom at each node. It was assumed that the boundary conditions at the blade fixing were like a cantilever beam. As the results of the numerical modelling process, the values of the first 10 bending natural frequencies and corresponding to them modes shapes of vibrations were determined for damage and undamaged states. The block Lanczos method has been used to calculate the modal parameters. A series of simulations were conducted. No artificial noise was introduced at this stage of research. The data were obtained at 200 nodal points, located on a straight line along the blade length. The blade model with the damage pattern is presented in Figure 4.  
The presented investigation concentrated only on the method for the detection of a delamination phenomenon. It is very characteristic and, at the same time, one of the most frequent types of damage for composite, especially laminated shells. The delamination means the separation of adjacent layers of composite and can be caused as a result of blade coating deformation during its motion. For this numerical study, a simple model of delamination was proposed. The concept used by the authors is associated with the phenomenon of zero tangential stress between separated layers in the damage zone. In the numerical model, this feature is simulated by reducing the shear modulus in the lamination plane (\(G_{XY}\)). The major problem in simulation process was determining the value of the shear modulus for a delaminated zone, which would provide an exact representation of the damage in the numerical model in the calculation of modal parameters with simultaneous easy implementation. For this purpose, an additional modal analysis of a straight cantilever beam with modelled damage was carried out. The obtained results were compared with the natural frequencies of the reference model. The assumed consistent of results was obtained when the shear modulus in the damaged area was lowered to 14% of its initial value. A more detailed description of the damage modeling method used can be found in [19].