## 3 Experimental Results  
An EMA was performed for each of the CLD structures considered with the commercial software \"ModalView\", obtaining frequency and modal damping for the first three modes. Frequency Response Functions in our bandwidth of 100 Hz were obtained with 4096 frequency lines, so the frequency resolution is lower than 0.025 Hz. Modal damping and eigenfrequencies were estimated with the Linear Square Complex Frequency Estimator (LSCF) using discrete-time z-model, which is a widely used frequency-domain modal parameter estimation method which provides higher accuracy, stability, and calculation speed than other methods [25; 26]. The modal shapes obtained for the beams tested are basically those for a pinned-pinned beam, although slight shifts of the vibration nodes were observed when the configurations were asymmetrical (B2 and C2). CLD patches not only provide structural damping, but also add mass and stiffness to the structure, which results in a small variation of modal frequencies. Figure 5 shows the value of the natural frequency of the first mode of vibration in ascending order for the different configurations analysed. In general, all configurations (B type especially) contribute more mass than stiffness, resulting in a small reduction in the natural frequency with hardly any influence on passenger comfort. Similar trends and percentage reductions in frequency can be found when analysing the second and third flexible modes. All values are gathered in Table 2.  
Figure 5: Natural frequencies of the first mode of vibration for the different configurations (ranked from lowest to highest). Modal damping deserves further consideration. If one considers CLD patches as a mere addition of material to increase modal damping of a lightweight structure, mass is a critical factor and the highest specific damping \(\overline{\xi}\) (damping per unit mass) should be sought. However, if the structural engineer manages to design the structure so that the constraining layer contributes to the global structural stiffness, the weight of the constraining layer would no longer be relevant and the maximum absolute damping \(\xi\) should be pursued. Figures 6-8 show the absolute and specific damping for the three flexible modes. All configurations increase structural damping significantly for all the modes. In the worst case (B4) for the first flexible mode, damping is four times higher than that of the reference beam (  
The type of constraining layer can be analysed by comparing configurations B3 and C6, with similar added mass (around 12 kg each) and the rest of parameters being identical. In all modes, C6 achieves a higher damping (52%, 70% and 107% higher in modes 1, 2 and 3, respectively), so it would be convenient to design the constraining layer in such a way as to increase the inertia of the section to enhance the performance of the viscoelastic layer. The effect of viscoelastic layer thickness can be studied by comparing configurations C3 and C7, with 2 and 1 mm viscoelastic layer thickness, respectively. It comes as a surprise that an increase in the viscoelastic layer thickness can be detrimental. Indeed, C3, with a 2 mm thick viscoelastic layer, reduces the structural damping of the three modes by about 30% with respect to C7. The influence of the location of the constraining layer is analysed by comparing configurations C1 and C2 (or, alternatively, B1 and B2 with identical conclusions). In this case, results depend on modal shape. The centred position of the patch maximises the modal damping of the first mode but not that of the second and third modes. This result was predictable as the dissipation of the viscoelastic layer is amplified with the deformation of the structure, which is larger at antinodes. The covered area is compared in configurations C1 (50%) and C3 (100%) or their analogues B1 and B3. It is obvious that a larger area covers antinodes of more vibration modes; therefore, the damping of modes 2 and 3 is greatly improved with 100% coverage.