# Vibroacoustic Assessment of an Innovative Composite Material for the Roof of a Coupe Car
## 4 Experimental-Numerical Correlation on FRF of a Real Component  
Experimental tests were conducted in order to acquire the frequency response functions at specific points on a component made of PP 23 CF, through the following steps:  
* the tested component is the central rear aerodynamic guard of the Alfa Romeo Giulia car, dimensions are 1370 \(\times\) 537 \(\times\) 2.5 mm;
* the component was suspended from a rigid frame by means of 50 cm long low stiffness elastic tie rods,
* the instrument that excites the structure is an instrumented hammer, with a load cell impedance of 3.96 \(\Omega\)
* the system response was recorded with a PCB HT 356B21 piezoelectric accelerometer.  
The accelerometer was glued in each point of analysis, and, in the same point, the component was excited with an instrumented hammer (Figure 4).  
Figure 3: Frequency response function of oscillating specimen: Identification of resonance peaks.  
For each point, three shots were given in the normal direction to the component (in case of an overload or an underload, the software automatically rejects the measurement), the hammer input and accelerometer output signals were post-processed with the LMS Test.Lab--Impact Testing software (Munich, Germany).  
Three blow repetitions are necessary for each acquisition point in order to evaluate the coherence function \(\gamma\), which must be close to 1 for the entire frequency range of interest, in the case under consideration from 0 to 400 Hz.  
Twenty FRF curves were exported, one for each acquisition point, in order to perform an experimental numerical correlation on a sufficient number of points.  
The Frequency Response calculation was performed through post-modal reconstruction (Real Eigenvalue Analysis--SOL 103-Nastran), exciting the component in a point and calculating the acceleration vs. frequency at the same point.  
The composite material was modeled as homogeneous and the preprocessing was carried out using the Altair HyperMesh software [21].  
The shelter components are all plastic made and were modeled by using two-dimensional shell elements.  
A mesh consisting mainly of Quad elements and a small percentage of Tria elements, with an average size of 3.5 mm was created (Figure 5).  
Figure 4: Instrumented hammer and shelter component.  
Figure 5: Aerodynamic guard mode with highlight of the adopted mesh.  
Numerical and experimental inertances, in the frequency range [0-400] Hz, are explicitly shown in Figure 6 for a couple of points.  
To numerically evaluate the numerical-experimental correlation, the Frequency Response Assurance Criterion (FRAC) was chosen (Equation (4)), its values ranging in the interval [0-1]: A FRAC value equal to 1 indicates an optimal correlation and values greater than 0.90 are considered satisfactory.  
\[FRAC=\frac{\left[\sum_{i=50 Hz}^{400 Hz}\left(FRF_{sp}(i)_{j,k}*FR_{num}(i)_{j,k} \right)\right]^{2}}{\left[\sum_{i=50 Hz}^{400 Hz}\left(FRF_{sp}(i)_{j,k}\right)^{ 2}\right]*\left[\sum_{i=50 Hz}^{400 Hz}\left(FRF_{num}(i)_{j,k}\right)^{2}\right]} \tag{4}\]  
In the case in question, the obtained FRAC values were greater than 0.9 for all points with a coherence function close to 1 (the coherence function \(\gamma^{2}\). is obtained by the ratio between two spectral density functions calculated from different experimental data). Such results allowed concluding that the virtual component, characterized as a homogeneous material, with the mechanical and damping properties measured experimentally, satisfactorily approximates reality.  
The next step is the modeling of the car roof of the Alfa Romeo 4C car.  
Figure 6: Numerical (black line) and experimental (red line) inertances vs. frequency (Hz) for the shelter component at points N. 13 and 14 (see Figure 4).