## 1 Introduction
In this paper, we propose an integrated verification approach [3; 4; 5] exploiting an innovative semiempirical Eldred-based source model with BEM propagation [6; 7] for building the jet acoustic pressure field, as well as a state-of-the-art hybrid FEM/statistical energy analysis (SEA) method adopted to combine the equipment's local deterministic responses with the mean value of the dynamic response of the launcher's major sections. In Figure 1, the logical structure of the whole integrated method is shown, with the acoustic field calculation feeding the structural dynamic simulation. Figure 1: The logical scheme of the integrated multidisciplinary approach used for the VEGA Consolidation and Evolution Program (VECEP) design verification process, described in this paper, is shown. The power of the proposed approach, with respect to other hybrid vibroacoustic methods, lies in its integration with the aeroacoustic component. In fact, a realistic model for the forcing pressure clearly implies a realistic reconstruction of the structural response in the operating condition considered. The concept of a space launcher can be, in some sense, elusive. It is thus worthy to try to define the range of applicability of the approach described in this work. In particular, the model used for reconstructing the acoustic pressure field acting on the structure and due to jet fluid dynamics aspects is general and independent from the type of the structure taken into account as well as from considering a horizontal or vertical launch. On the other hand, the hybrid techniques describing the response of the structure to the load cannot be reliable for geometries including wings, because of the complications arising in the model and the possible fall down of the diffuse-field assumption. The semiempirical approach for reconstructing the acoustical pressure component of the rocket jet is described in Section 2. It is an improvement of the Eldred Standard model, based on heuristic assumptions and scaling laws, properly tuned against experimental data from different rocket engines [8; 9; 10; 11]. In this simple model, in order to determine a realistic equivalent noise source, several parameters, such as the vehicle geometry or launch pad configurations, have to be taken into account. Several hybrid methods have been proposed for overcoming this limit [12; 13], and the new formulation contains an explicit expression for the acoustic pressure of each noise source, in terms of amplitude and phase, in order to account for correlation effects and propagate the signal using a wave equation. The noise prediction obtained with the revised Eldred-based model has thus been used for formulating an empirical/BEM approach that allows us to evaluate the scattering effects, which, summed with the direct, correlated acoustical pressure, is exploited for the prediction of the aeroacoustics loads of the VEGA launch vehicle at lift-off. The hybrid FEM/SEA vibroacoustic approach is described and validated in Section 3. The implemented analysis resorts to a FEM solver to extract the modal parameters associated to the deterministic subsystems of the VEGA interstages. The development of the statistical subsystems and the set-up of the global hybrid models are realised within a numerical environment, formerly devoted to SEA methodology only, in which the required dynamic analysis is also performed. The structural and acoustical models of the interstages are validated through a comparison with theoretical and numerical estimates. As required for the assessment of the equipment qualification status, the activity is finalized with the delivery of the dynamic response database, numerically generated by applying the acoustic pressure field to the interstage validated models. Two sections, dealing with the discussion of the results and some concluding remarks, close the paper.