# A Novel Optimization Framework to Replicate the Vibro-Acoustics Response of an Aircraft Fuselage
## 3 CAD/FEM Modeling
### Reference Case (RC) and Simplified Cases (SC)  
The so obtained vibro-acoustic FEM model was preliminary solved by considering as acoustic load the pressure on the external skin calculated by aeroacoustic calculations (Figure 4). This simulation was termed as Reference Case (RC) because it provided the benchmark to assess the Simplified Cases (SCs). Such pressure distribution outside the fuselage was obtained by aeroacoustic simulations, based on the integral formulation of Flowcs Williams and Hawkings [8], and considered the rotating engine rotors, at the first Blade Passage Frequency (1 BPF), as the only noise contributor providing periodic low frequency loads on the structure. It was considered just the 1 BPF because it was the most relevant under cruise flight condition.  
From Figure 4, it can be qualitatively noticed that the acoustic pressure load shape was caused by the phase shift of the engine rotors (an arbitrary non-null value was selected in this case), and the increment of the load amplitude in the axial direction, as a consequence of the distance reduction from the rotors position. The circumferential distribution of pressure loads presents a complex pattern, clearly variable as a function of the imposed phase shift.  
More in general, given the model being available, the calculation of additional frequencies or noise contributors does not impose additional complications apart from the calculation time.  
Subsequently, the boundary condition corresponding to the pressure distribution was removed from the FEM model and a set of acoustic sources and microphones (monitoring points) was added. Such modified FEM model, after a vibro-acoustic coupled analysis, provided the results to be used as input for the MDO procedure.  
In particular, a given set of acoustic sources and two different sets of microphones were considered, termed in the followings as SCs: SC1 and SC2. The two SCs correspond to two attempts to replicate  
Figure 4: Sound pressure field on the fuselage considered as boundary condition for the Reference Case (RC) (the engine is located on the right side of Figure 4c). (a) isometric view; (b) front view; (c) lateral view.  
the RC, namely, to replicate the realistic reference solution in terms of acoustic pressure outside the fuselage and, consequentially, in terms of vibro-acoustic response of the structure.  
Figure 5 shows the number (four) and positions of the acoustic monopole sources designed to try reproducing the reference sound field and providing the input for the MDO iterations.  
Figure 6 highlights number and position of the microphones required to measure the Acoustic Intensities (AIs) outside the fuselage. Such microphones were required in order to monitor the pressure field on the fuselage surface for each MDO iteration. Two kinds of positioning were considered comprising either 3 or 5 rings having 6 microphones each, for a total of either 18 or 30 microphones.  
Figure 5: Monopole sources positions (in red) outside the fuselage.  
Figure 6: Microphones positions (in yellow) outside the fuselage representing the output positions for the optimization process: configuration with **(a)** 18 and **(b)** 30 microphones.  
Such monopoles and microphones were adopted to create two SCs (Figures 6 and 7), i.e.,  
* SC1 (Figure 7a), comprising 18 output microphones,
* SC2 (Figure 7b), comprising 30 output microphones.  
Both SCs comprised 4 monopole sources positioned as shown in Figure 5.