Acoustic design of boundary segments in aircraft fuselages using topology optimization and a specialized acoustic pressure function

Abstract

In most aviation applications, a major cost benefit can be achieved by a reduction of the system weight. Often the acoustic properties of the fuselage structure are not in the focus of the primary design process, too. A final correction of poor acoustic properties is usually done using insulation mats in the chamber between the primary and secondary shell. It is plausible that a more sophisticated material distribution in that area can result in a substantially reduced weight. Topology optimization is a well-known approach to reduce material of compliant structures. In this paper an adaption of this method to acoustic problems is investigated. The gap full of insulation mats is suitably parameterized to achieve different material distributions. To find advantageous configurations, the objective in the underlying topology optimization is chosen to obtain good acoustic pressure patterns in the aircraft cabin. An important task in the optimization is an adequate Finite Element model of the system. This can usually not be obtained from commercially available programs due to the lack of special sensitivity data with respect to the design parameters. Therefore an appropriate implementation of the algorithm has been done, exploiting the vector and matrix capabilities in the MATLAB environment. Finally some new aspects of the Finite Element implementation will also be presented, since they are interesting on its own and can be generalized to efficiently solve other partial differential equations as well.