## 3 Results
### Calculations of the Reference Frequencies
Indeed, the modal shape follows the rotations of the material with respect to the clamped boundaries. Furthermore, the discrepancy between the first resonant frequencies for the two mass positions is inversely proportional to the mass of the concentrated mass, while it is enhanced by the thickness of the laminate. An added mass reduces the resonant frequencies, and higher values of concentrated mass lead to higher reduction of the resonances, thus flattening any discrepancy. On the contrary, the thickness plays a key role in the bending stiffness of the laminate, which in turn affects the resonant frequency. As the thickness increases, the first resonant frequencies for the two mass spots proportionally increase and so does the discrepancy. It is the case of the woven laminate, whose anisotropy is particularly limited but still recognizable, as shown in Table 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{0}^{\circ}\) & \(\mathbf{30}^{\circ}\) & \(\mathbf{60}^{\circ}\) & \(\mathbf{90}^{\circ}\) \\ \hline \(f_{ref}\) [Hz] & 850.2 & 1117.4 & 1361.7 & 1191.8 \\ \(f_{ref,m1}\) [Hz] & 817.3 & 1070.3 & 1283.9 & 1126.8 \\ \(f_{ref,m2}\) [Hz] & 808.1 & 1054.9 & 1283.2 & 1136.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: First resonant frequency values with and without the 1 g mass load of the anti-symmetric plate (\([30^{\circ},\,-30^{\circ},\,-30^{\circ}]\)) for different material orientations. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{0}^{\circ}\) & \(\mathbf{15}^{\circ}\) & \(\mathbf{30}^{\circ}\) & \(\mathbf{45}^{\circ}\) \\ \hline \(f_{ref}\) [Hz] & 1793.8 & 1757.9 & 1686.7 & 1650.5 \\ \(f_{ref,m1}\) [Hz] & 1738.0 & 1702.0 & 1633.8 & 1600.5 \\ \(f_{ref,m2}\) [Hz] & 1738.0 & 1705.2 & 1636.6 & 1600.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: First resonant frequency values with and without the 1 g mass load of the woven fabric plate (\([0^{\circ},\,0^{\circ},\,0^{\circ},\,0^{\circ}]\)) for different material orientations. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{0}^{\circ}\) & \(\mathbf{30}^{\circ}\) & \(\mathbf{60}^{\circ}\) & \(\mathbf{90}^{\circ}\) \\ \hline \(f_{ref}\) [Hz] & 505.1 & 535.5 & 773.1 & 948.3 \\ \(f_{ref,m1}\) [Hz] & 472.3 & 507.8 & 720.8 & 855.2 \\ \(f_{ref,m2}\) [Hz] & 472.3 & 494.0 & 705.9 & 855.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: First resonant frequency values with and without the 1 g mass load of the unidirectional plate (\([0^{\circ},\,0^{\circ},\,0^{\circ},\,0^{\circ}]\)) for different material orientations. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{0}^{\circ}\) & \(\mathbf{30}^{\circ}\) & \(\mathbf{60}^{\circ}\) & \(\mathbf{90}^{\circ}\) \\ \hline \(f_{ref}\) [Hz] & 850.2 & 1117.4 & 1361.7 & 1191.8 \\ \(f_{ref,m1}\) [Hz] & 817.3 & 1070.3 & 1283.9 & 1126.8 \\ \(f_{ref,m2}\) [Hz] & 808.1 & 1054.9 & 1283.2 & 1136.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: First resonant frequency values with and without the 1 g mass load of the symmetric plate (\([30^{\circ},\,-30^{\circ},\,-30^{\circ},\,30^{\circ}]\)) for different material orientations. Finally, it can be argued that as the material properties do not change after a rotation of 90\({}^{\circ}\) for the unidirectional reinforcement laminates or 45\({}^{\circ}\) in the case of woven fabric, further information can be considered within the optimization process without the need of other replications of the first resonant frequency measure. In particular, in the case of unidirectional reinforced laminates, the results obtained for 30\({}^{\circ}\) and 60\({}^{\circ}\) are respectively equal to those obtained for rotations equal to 150\({}^{\circ}\) and 120\({}^{\circ}\), respectively. However, the results obtained with the concentrated mass must be switched, as the modal shape follows the rotations of the material with respect to the clamped boundaries. The same can be applied to the woven fabric, thus extending the acquired information to the range 45\({}^{\circ}\)-90\({}^{\circ}\).