## 3 Hybrid FEM/SEA Model and Interstage Response Analysis  
As pointed out in the introduction, the objective of this work is to predict the acceleration response level at the equipment and payload location, for subsequent verification of their qualification status. In addition, the dynamic average response of the VEGA interstage interfaces IS01, IS12 and IS23 to the acoustic field generated at lift-off by the P120 engine has been calculated with the innovative approach described in the previous section. A numerical prediction has been obtained through the development of hybrid FEM/SEA models and their analysis in the 100-1600 Hz frequency range using the commercial code VAOne [18], in order to overcome the limitation of deterministic tools in the investigated frequency range. The fourth section of VEGA, constituted by the interstage IS34, the Attitude Vernier Upper Module (AVUM) and the Fairing, was left out from the numerical investigation because it has been unchanged with respect to the old configuration. The large frequency range spread of the pressure power spectra motivates the need for a vibroacoustic response analysis accounting for all the frequency content of the main external pressure field to avoid underestimating the equipment's and components' acceleration levels. Despite the relatively high skin thickness and the opportunity to perform the analysis on each component separately, the large dimensions of the VEGA interstages still require the involvement of a large number of structural modes, not to mention at all the even higher modal density of the coupled interior acoustic cavities. As a consequence, above 400/500 Hz, the FEM technique turns out to be computationally unfeasible even when resorting to modal superposition procedures, and the SEA approach becomes more appropriate for acquiring the responses of both the structure and the acoustic cavity. As a matter of fact, SEA represents systems in terms of a number of coupled subsystems, taking into account the global energy trade-off due to their interaction, namely, energy storage, transmission and dissipation. The parameters in SEA equations are typically obtained with certain statistical assumptions about the dynamic properties of each subsystem. For running the calculations, the commercial code VAOne has been used. The code allows for a complete range of analysis because different solution methods and modules are available, specifically, FEM, BEM and SEA. The capabilities in dealing with any kind of dynamic problem are even enlarged by the option to develop hybrid models, in which all available methodologies are combined. The development of structural models entirely based on a SEA approach was restricted by the need to simulate the equipment as a lumped mass, connected to the main structure throughout rigid links. These components are not suitable for SEA modeling because they have no modal behavior by definition, while a large modal participation is required for a SEA model to be accurate. The adoption of a hybrid approach was mandatory for the monitoring of the equipment acceleration levels, in order to verify their qualification status. Consequently, for all interstages, a full SEA model could not be developed, and a careful identification of the number and extension of the interstage parts to be modeled as FEM subsystems was required to avoid building up a model unsuitable for a SEA approach. Moreover, all the external and internal interfaces have been modeledas FEM subsystems to retain all their dynamic contributions, otherwise ignored by using a SEA \"beam\"-type subsystem for their simulation. The correct balance among the different type of subsystems (either SEA or FEM) was essential to allow a fairly quick analysis with no penalties in terms of accuracy. General rules to check the accuracy of a SEA subsystem are based on the following concepts, applicable to the frequency bands chosen for the analysis:  
* A mode count of no less than 5. * A model overlap factor (MOF) greater than or equal to the unitary value.