Significant interior noise and vibrations in aircraft cabins are generated by the turbulent flow over the fuselage. The turbulent boundary layer (TBL) excitation is the most important noise source for jet powered aircraft during cruise flight. Reduced levels of interior noise are desirable both for comfort and health reasons. However, to efficiently design noise control systems, and to design new and optimized structures that are more efficient in the noise reduction, a clearer understanding of the sound radiation and transmission mechanisms is crucial. This task is far from being straightforward, mainly due to the complexity of the system consisted by the aircraft fuselage, and all the sound transmission mechanisms involved in a such complex environment. The present work aims to give a contribution for the understanding of these mechanisms. For that, a coupled aero-vibro-acoustic analytical model for the prediction of the TBL-induced noise and vibration in aircraft is developed. Closed form analytical expressions are obtained to predict the structural vibration levels, noise radiated from the structure and interior sound pressure levels.

As well as the physical system under study, the mathematical model is composed by three distinct submodels:​ the aerodynamic model, which describe the TBL wall pressure fluctuations over the aircraft fuselage skin, the structural model, representing the aircraft panels structural vibration, and the acoustic model, which represents the acoustic pressure field in the aircraft cabin. These individual submodels are then mathematically coupled, such that the effect of the first submodel can be observed in the second and third submodels. As a random process, the TBL wall pressure is statistically described in terms of the power spectral density (PSD), by the use of empirical models. The structural response of the aircraft panels is defined using the linear plate and shell theories. The wave equation is used to define the cabin acoustic field. The displacement of the panels and the interior acoustic pressure are represented, respectively, through the panel and acoustic natural modes. The models were developed for the Cartesian and the cylindrical coordinates systems, respectively, for a rectangular and a cylindrical cabin. The flexible structure can be composed by one or several panels, which are considered to be simply supported. For both the structural and acoustic models, a damping factor was added in the equations of dynamics, in order to account for the structural and acoustic damping of the respective subsystems.

Results for the prediction of the vibration level of the aircraft panels, radiated sound power, and interior sound pressure levels in the aircraft cabin are obtained. The analytical models are validated through the successful comparison with several independent experimental studies. The TBL empirical models existent nowadays provide different predictions for the TBL wall pressure fluctuations PSD. For this reason, it is important to understand the range of conditions that different wall pressure fluctuations PSD produce in the noise radiation problem. To accomplish that, a sensitivity analysis on the sound radiated by the structural panels to the change of TBL parameters is undertaken. The models are able to predict localized and average values of interior noise level and structural vibration level. It is shown that average values and localized values can be very dissimilar from each other. Usually, the average values are assumed to be representative of the physical system response. This can be of particular importance, for instance, in the noise reduction systems design, where the accurate information about the system behavior is crucial. It is shown that the number of structural and acoustic modes considered in the analysis can greatly affect the accuracy of the predicted quantities.