The MDE Method for Aircraft Cabin Interior Noise Prediction

The matrix difference equation (MDE) method is a finite-element approach to computing aircraft cabin interior noise levels resulting from external sources such as engines and turbulent boundary layers. The computer code is applicable to coupled structural-acoustic models representing the fuselage structure and the air inside. Nodal displacements are the unknown variables for both the structural and acoustic components of the model, and compatibility at the interface is satisfied by equating normal displacements. The acoustic element is a structural element modified to reflect the properties of a gas. A transformation eliminates zero-frequency modes so that the size of the free-vibration eigensolution is the same as it would be if pressure instead of displacement were the acoustic variable. Forced vibration analysis is accomplished by the modal frequency response method. The analysis benefits from the assumption that the fuselage can be considered spatially periodic (composed of identical substructures), so that the user models only a single substructure, and computing cost is typically less than 1/50 of the cost of conventional finite-element analysis. An auxiliary code will enable the user to modify the results to account for the presence of nonperiodic features, such as heavy bulkheads. Correlation of MDE results with classical theory and test data is presented as verification. The method is expected to provide a design tool for reducing cabin noise levels for conventionally powered and advanced propeller-driven aircraft.