## 4 Results and Discussion  
### Sound Transmission Loss  
Figure 9 shows the frequency response function measured on the beam cut in the \(x\)-direction. For each natural frequency (grey circles in Figure 9a), it is possible to compute the relevant bending stiffness points (grey circles in Figure 9b) as a function of frequency. The solid line in Figure 9b is the reconstructed apparent bending stiffness curve computed by applying the LS method to the experimental points. The same procedure has been adopted for the beam cut in the \(y\)-direction (Figure 10). The two apparent bending stiffness curves predicted in the \(x\)- and \(y\)-direction are compared and composed in Figure 11. The composed apparent bending stiffness \(D_{avg}\) has been obtained from the average on the in-plane angle \(\theta\) of the following function [29]:  
\[D_{a}^{\prime}\left(\theta\right)=\left[{D_{a,x}^{\prime}}^{1/2}\cos^{2}\left( \theta\right)+{D_{a,y}^{\prime}}^{1/2}\sin^{2}\left(\theta\right)\right]^{2}. \tag{24}\]  
In computing the sound transmission coefficient \(\tau_{d}\), the \(\theta\)-dependent bending stiffness function should be used and \(\tau\left(\phi,\theta\right)\) should be integrated over the in-plane angle to obtain the sound transmission behavior of the whole structure. Figure 8: Experimental measurement of the core shear modulus: (**a**) specimen and clamping system; (**b**) test setup. The structural reverberation time technique has been used to measure the total loss factor necessary to calculate the sound transmission coefficient. The average loss factor has been computed by taking into account the results of five measurements carried out on randomly-distributed positions. The results of this procedure are reported in Figure 12. The loss factor varies from a maximum of 5.5% in the low frequency range to a minimum value of 0.5% for frequencies above 400 Hz. Figure 10: \(y\)-direction. (**a**) Measured transfer function and natural frequencies (grey circles); (**b**) bending stiffness from measured natural frequencies (grey circles) and approximated by the LS method (solid line). Figure 9: \(x\)-direction. (**a**) Measured transfer function and natural frequencies (grey circles); (**b**) bending stiffness from measured natural frequencies (grey circles) and approximated by the LS method (solid line). The tested structure almost behaves like an isotropic material, and no significant difference has been found between computing \(\tau_{d}\) from a single, averaged \(D_{avg}\) function or a \(\theta\)-dependent \(D_{a}^{\prime}\left(\theta\right)\) function. Either approach can therefore be used to derive the \(R\) index. Figure 13 reports the comparison between the predicted sound transmission loss (total loss factor as in Figure 12) and measurements in sound transmission suites. The agreement between predicted and measured curves is good above 200 Hz, while there is a discrepancy below this frequency due to the so-called 'baffle effect' [24]. The panel has a finite size and does not cover the entire surface of the wall dividing the two sound transmission suites. Since the sound transmission coefficient (Equation (8)) has been, in principle, derived for infinite panels, a correction may be required in the low frequency range. However, it is worth remarking how this simple technique proves to be extremely valid in predicting the location, extension and depth of the coincidence region at about 400 Hz. Figure 11: Comparison of bending stiffness curves in the \(x\)- and \(y\)-direction and their composition (\(D_{avg}\)). Figure 12: Loss factor measured with the structural reverberation time technique. For strongly-orthotropic structures, the coincidence effect is usually located in different frequency regions according to the in-plane angle. In this case, using a single 'average' apparent bending stiffness curve is not acceptable, and the \(\theta\)-dependent bending stiffness function should be used instead.