# A Novel Optimization Framework to Replicate the Vibro-Acoustics Response of an Aircraft Fuselage
## 1 Introduction  
Nowadays, an accurate evaluation of noise generation and propagation has become a key concern, especially in the areas in which the comfort for end users has become a turning point. An increasing interest of aerospace and automotive industries for the passengers' comfort has been providing the framework in which these issues have acquired a prominent role. The typical topics to be tackled for investigations of noise and vibrations of vehicles, aircraft, space launchers, etc. deal with aerodynamically generated noise, engine noise, Passive Noise Control (PNC), Active Noise Control (ANC) and assessment of acoustic properties of innovative materials [1]. The reduction of acoustic emissions and the improvement of interior comfort are on the path of all major industries of the transport system, having a direct impact on customer satisfaction and, consequently, on the commercial success of new products. Nowadays, the aeronautics industry requires several experimental tests during the designing processes that, very often, present huge costs and generally are not simple to carry out with a reasonable accuracy. In this work, a Finite Element Method-Multi-Disciplinary Optimization (FEM-MDO) framework has been proposed to characterize sets of acoustic sources that replicate the sound field produced by the real engines on an aircraft fuselage mock-up. This procedure would enable to set up ground experimental tests on aircraft components, useful to replicate their vibro-acoustic performances as iftested in flight. More in general, it can also be used as a reference tool to design simplified tests for complex problems. Similar approaches in which simplified acoustic sources were used to simulate more complex acoustic fields can be found in literature, e.g., the noise generated by rocket engines in [2; 3; 4; 5]. In fact, in these works a semi-empirical jet noise model has been exploited and adapted for reconstructing the experimental acoustic near field on the external surface of a space launcher, allowing an affordable vibro-acoustic assessment based on the achieved pressure excitation. The reference theory to predict the noise radiated by rotors can be found in [6; 7], in which [PERSON] originally developed the first aeroacoustics analogy that, in the last decades, has been extensively applied in numerical aeroacoustics to reduce the complex sound sources to simple emitter types. In general, aeroacoustic analogies were derived from the compressible Navier-Stokes equations, rearranged into forms of the inhomogeneous acoustic wave equation. Some approximations were introduced to make the source terms independent of the acoustic variables and, in this way, linearized equations were derived to describe the propagation of the acoustic waves in a homogeneous resting medium. The original formulation of Lighthill was extended by [PERSON] [8] to take into account vibrating solid surfaces, by rearranging the Navier-Stokes equations with introduction of source terms composed by:  
* quadrupole sources, generated by the turbulence of the fluid;
* dipole sources, caused by fluctuations of the fluid-structural interaction forces;
* monopole sources, generated by mass fluctuations. These theories do not provide any indication about the positioning of sources that commonly are characterized by means of Computational Fluid Dynamics (CFD) simulations and located in correspondence of the geometrical central axis of the engine rotors. These theories are also still inefficient under near field conditions. Thus, it is commonly necessary to proceed numerically to determine type, number and position of the acoustic sources in the most complicated cases. Such numerical procedures allow to approximately replicate the real acoustic pressure fields generated by the engines via ordinary acoustic sources. In this way, the experimental testing could be carried out either in anechoic or semi anechoic environments with the emulated acoustic field imposed by loudspeakers.