## 4 Analysis of Relevant Influencing Parameters
### Effect of Delaminations
#### 4.3.2 Reliability of Frequency Calculations for Delaminated LG Specimens  
The application of Equations (12)-(14) to the examined LG beams, where even marked frequency reductions can be expected, as compared to the theoretical values of LG beams with uniform PVB bonding. Generally, the MoE of partially delaminated beams (\(E_{d}\)) is linearly dependent on the delaminated area, when compared to the total bonding surface (see Equation (13)). As far as the effective MoE is taken into account for the examined LG beams (i.e., Figure 17b), it is thus possible to expect a MoE decrease in the order of 30%, for even a limited portion of delaminated interlayer. Such a MoE variation turns out in a marked variation of the bending stiffness for the composite LG beam, and at the same time reflects on a different shear stiffness from the interlayer in use (i.e., Figure 3), thus representing a relevant influencing parameter for calculations. A parametric study was hence carried out on selected configurations in order to assess the reliability of Equations (12)-(14) for simple analytical calculations on delaminated LG beams. In accordance with Figure 18, more in detail, schematic delaminations were defined, to reproduce--even in a simplified way--some of the on-site qualitative observations from the experimental tests. In doing so, symmetry was taken into account for all of the possible configurations, thus resulting in:  
- Scheme D1: \(A_{d,tot}=2A_{d,1}\) delaminated surface close to each restraint, where \(A_{d,1}=b\times d\);  
- Scheme D2: similar to D1, but with \(A_{d,tot}=2A_{d,2}\) and \(A_{d,2}=b\times 2d\) close to each restraint;  
- Scheme D3: like D2, with \(A_{d,tot}=2A_{d,2}+2A_{d,3}\) and \(A_{d,3}=s\times b\) (\(s=30\), \(60\) and \(90\) mm); and,  
- Scheme D4: inclusive of delamination along the longitudinal edges, thus \(A_{d,tot}=2A_{d,2}+2A_{d,A}\), with \(A_{d,A}=t\times L_{0}\) (\(t=15\), \(30\), \(45\) mm, that is \(\approx\)\(b/10\), \(\approx\)\(b/5\) and \(\approx\)\(b/3\) for the selected specimens). The analytical estimates of fundamental frequencies were carried out with the dynamic thickness \(h_{\mathit{ef}}\) and iterative approach of Section 2, with the additional set of iterations due to a decreasing MoE (with increasing the delamination surface \(A_{d}\)). The same iterative approach includes the effect of mechanical restraints, in accordance with Equation (11). The support of full 3D solid models from ABAQUS was also taken into account. In the latter case, the choice of full 3D models was suggested by the need of including possible delaminations in several regions of interest (see Figure 19). The glass and interlayer foils were rigidly connected via \"_tie_\" constraints, in order to ensure a rigid mechanical connection for the involved surfaces. In the presence of delaminated regions, moreover, additional contact interactions were used between the involved layers. In Figure 19a, an example is proposed for the D4 scheme. The mechanical restraints were then reproduced in the form of equivalent axial and rotational springs (with \(K_{r}>0\) and \(K_{s}=\infty\)). These springs were connected to reference RP nodes, and then restrained to each LG beam with the use of additional \"_coupling_\" constraints, thus reproducing the actual effect of the steel point-fixings in use (see Figure 19b)). Frequency analyses were thus carried out on a wide set of configurations of LG beams. In Figure 19c, an example of typical deformed shape is shown (\(n=1\)). Through the FE parametric calculations, variations were made in terms of span (\(L\)) and delaminated region (\(A_{d}\)). Figure 20 reports some of the collected results, for a LG beam with \(L=2.65\) m and \(d=0.07\) m, \(10\) mm and \(0.76\) mm the thicknesses of glass and PVB layers, respectively.