# Delamination Assessment in Composite Laminates through Local Impulse Excitation Technique (IET)
## 3 Results
### Experimental Investigations on Intact Plates  
Figure 6 shows the resultant first resonant frequencies of the undamaged plates as a function of the parameter \(\frac{1}{2\pi a^{2}}\cdot\sqrt{\frac{\text{TrD}}{\rho\text{h}}}\). As shown, for low values of the parameter \(\frac{1}{2\pi a^{2}}\cdot\sqrt{\frac{\text{TrD}}{\rho\text{h}}}\), the measured frequencies are linearly dependent on the parameter according to Equation (3). When the parameter \(\frac{1}{2\pi a^{2}}\cdot\sqrt{\frac{\text{TrD}}{\rho\text{h}}}\) has very high values, that is, for stiffer materials and smaller devices, the relationship deviates from the linearity with a decreasing slope, suggesting a change in the constraint provided by the device and, in turn, a change in the effectiveness of the device in isolating the mechanical vibrations. Focusing on the linear field, the slope \(\lambda\) is equal to 15.4, which suggests that the boundary conditions of the device approximate the condition of perfect clamping, although with some discrepancy, and are between the simply supporting and the clamping cases. The compliance of the rubber seal plays a key role in this regard, as also observed in previous investigations [20], given its noninfinite stiffness. It is also worth noting that the experimental results are linearly interpolated with a positive intercept equal to 120.5 Hz, which can be attributed to the in-plane spurious stresses induced by the vacuum clamping system, which increase the resultant frequencies. It is worth noting that, according to Figure 6, specific values for the slope and the intercept can be determined for each material, which can, accordingly, better describe the relationship between the first resonant frequency and the parameter \(\frac{1}{2\pi a^{2}}\sqrt{\frac{TD}{\rho\cdot H}}\). However, since the goal is to identify an FE model that is generally valid, a global slope \(\lambda\) equal to 15.4 and a global intercept equal to 120.5 Hz were retained. The deviation from the linearity shown In Figure 6 suggests that the constraint effectiveness, that is, the capacity to isolate the mechanical vibrations, depends on the material properties of the plate and on the size of the device. However, it must also be noted that the computation of the FRFs and, accordingly, of the first resonant frequency depends on the acquired signal. As the same input energy has been provided by the controlled impactor, the higher the flexural stiffness, the lower the resulting out-of-plane displacement, which, in turn, affects the FRF calculation. Figure 7 shows the acquired displacement signals and the resulting FRFs for the 50 \(\times\) 50 mm device. In particular, Figure 7 reports the results of the unidirectional plate, Figure 7 presents the results of the plain weave plate, Figure 7 presents the results of the twill 2 \(\times\) 2 carbon plate and Figure 7 presents the results for the twill 2 \(\times\) 2 glass plate. As shown in Figure 7, as the flexural stiffness increases, the out-of-plane displacement decreases, and the plate vibrations quickly end. In this regard, the damping properties of the material, which are mainly governed by the fiber volume fraction of the composite, also play a crucial role, affecting the peak broadening in the FRF. For the twill 2 \(\times\) 2 carbon plate, the out-of-plane displacement is almost comparable with the measurement noise and, accordingly, the FRF does not show a clear and evident peak. According to Figure 7, the power amplitude of the signal must overcome the power amplitude due to the noise of at least one order of magnitude. It is worth noting that, with the vibrations of the twill 2 \(\times\) 2 carbon plate consistently being limited over time, as shown in Figure 7, a similar FRF would be obtained through a microphone. As such, the limited vibrations over time affect the computation of the first resonant frequency. As the material flexural stiffness increases, the impulse energy must increase in order to guarantee sufficient oscillations over time.