## 2 Methods
### Modal Shape Information through Mass Position  
The proposed approach is based on a recently presented experimental methodology, which allows nondestructively assessing local elastic properties of composite laminates (K  
In the case of anisotropic materials, the modal shape is particularly dependent on the elastic parameters. For anisotropic material, the isolines of the modal shape are not necessarily parallel to the clamped boundaries. For instance, it is the case of an orthotropic material whose axes of orthotropy are not parallel to the boundaries. As reported in [13], and as shown in Figure 3, with reference to a unidirectional fiber plate, the first mode shape rotates in accordance with the orientation of the unidirectional reinforcement with respect to the \(x\) axis. In particular, for \(0^{\circ}\) and \(90^{\circ}\), material axes of orthotropy are parallel to the boundaries and so the isolines of the modal shape. Instead, for \(30^{\circ}\) and \(60^{\circ}\), whereas the material anisotropy is enhanced, the isolines are not parallel to the boundaries. This also shows that the modal shape strictly depends on the material properties and on its anisotropy. As the modal shape relates to the material anisotropy, information on the modal shape can be exploited to assess the elastic parameters with increased accuracy and robustness. To this aim, a concentrated mass can be adopted. Two locations are sufficient to investigate the isolines of the first modal shape and hence the material anisotropy. In particular, the two positions are to be symmetric with respect to one of the axes of symmetry of the rectangle, while not lying on the other axis. For an example of mass locations, the reader can refer to Figure 4.  
Figure 2: Experimental setup adopted in [13], with (**a**) and (**b**) dimensions of the retained rectangular region. Here, it is assumed that the first resonant frequency is measured through a microphone, which allows avoiding the contribution of the added mass of the accelerometer. When the isolines are not parallel to the boundaries, the modal displacement is different in correspondence of the two mass locations. As a consequence, the reduction of the first resonant frequency is different. Instead, when the isolines are parallel to the clamped boundaries, the first resonant frequency equally decreases, as the two mass positions are symmetric with respect to one of the axes of the rectangular plate. Thus, the discrepancy between the reductions of the first resonant frequency due to the two mass locations represents a measure of the material anisotropy. The methodology presented in [13] is completed as follows:  
1. Isolate a rectangular region of the component through a specific equipment, which clamps the extremities of the region without damaging the material;  
Figure 4: Example of mass spots symmetric with respect to one of the axes of the rectangular plate. Figure 3: Mode shape with contour lines at different orientations of the unidirectional reinforcement with respect to the x axis: (**a**) \(0^{\circ}\); (**b**) \(30^{\circ}\); (**c**) \(60^{\circ}\); and (**d**) \(90^{\circ}\). 2. Measure the first resonant frequency of the retained region, \(f_{ref,i}\), through the Impulse Excitation Technique;
3. Measure the first resonant frequency for each location of the concentrated mass, \(f_{ref,m1,i}\) and \(f_{ref,m2,i}\);
4. Repeat the frequency measurements after rotating the clamping system with respect to the material;
5. Assess the elastic properties of the investigated region from the measured resonant frequencies through an optimization process.