Shape Optimization of Cylindrical Shell for Interior Noise

In this paper an analytic method is used to solve for the cross spectral density of the interior acoustic response of a cylinder with nonuniform thickness subjected to turbulent boundary layer excitation. The cylinder is of honeycomb core construction with the thickness of the core material expressed as a cosine series in the circumferential direction. The coe cients of this series are used as the design variable in the optimization study. The objective function is the space and frequency averaged acoustic response. Results con rm the presence of multiple local minima as previously reported and demonstrate the potential for modest noise reduction. Introduction Aircraft interior noise levels have been an ongoing concern to airline operators and aircraft manufacturers for many years. The concerns have primarily been those of speech interference, crew fatigue, and passenger comfort, the latter arising primarily in private/business aircraft and rst class accommodations. Though there are currently no regulations on interior noise levels, airline operators have required guarantees from manufacturers on these levels. Some primary sources of interior noise that are currently being studied due to their strong interaction with aircraft structures are propeller, jet, boundary layer, and turbine noise, the latter being a primarily structure borne noise associated with rotor imbalances. Both propeller and turbine noise are primarily tonal in nature and have been the object of several recent structural acoustic optimization investigations. Cunefare et. al. [1,2] have been working to develop the tools and methodology for performing structuralacoustic optimization with acoustic objectives and constraints using commercial nite and boundary element software. Most of their structures were typical ring frame and stringer sti ened shells and fuselages subjected to either propeller or engine excitation. They demonstrated the ability to obtain modest amounts of noise reductions in many of the structures they studied with little or no weight penalty. Another observation from their work was that the acoustic objective function had many local minima and thus all of their results were reported as ranges. The level of noise reduction obtained in all their investigations varied widely depending on the initial design state. One of their rst reported results was for a thin aluminum monocoque shell and of particular interest to this investigation. In this study the shell was divided circumferentially into eighteen strips. The thicknesses of the shell within each of these areas became the design variables in the optimization study. For this idealized structure subjected to narrow band propeller noise interior noise reductions of 17 to 24 dB were obtained. Though this type of structural tailoring is impractical on thin isotropic material, the results were very good. The use of honeycomb core materials in commercial aircraft o er some signi cant advantages over aluminum, however, several disadvantages are also evident. An all-composite honeycomb core structure tends to have inherently lighter damping than its aluminum counterpart. The result of this is a potential for higher noise levels in the aircraft interiors. Several investigations whose objective was to improve the structural acoustic performance of honeycomb core structures have since been reported. Tang et. al. [3,4], in a classical parametric study, showed that `very' thick honeycomb structures had a more favorable high frequency transmission loss characteristic than either metallic, composite, or `thin' honeycomb structures. This appeared to be a phenomenon related to the ratio of the membrane and bending wave speeds. The prospect of using the ability to tailor this form of construction to reduce the low frequency interior noise levels of aircraft cabins has been investigated by Fernholz and Robinson [5,6]. They used the lamination angles of the inner and outer face sheets of the honeycomb side walls of an aircraft fuselage as design variables. Results demonstrated that a modest two to three dB of noise reduction was obtainable for interior noise generated by structural excitation. The present investigation will explore both the potential for interior noise reduction and the nature of the design space in thick honeycomb shells subjected to turbulent boundary layer (TBL) excitation where the honeycomb core thickness is the design variable. Speci cally, an analytic solution for the interior noise of a thick honeycomb core shell will be obtained for the case when the shell core thickness is expanded in a cosine series as Hcore( ) = hc + hc F ( ) = hc + hc nmax X