Effect of local impedance variation and non-linearity on multiple tone attenuation

摘要

An iterative Finite Element Method (FEM) is introduced for prediction of attenuation in a duct in which acoustic lining impedance depends on local grazing flow Mach number and overall local sound pressure level. A general approach is described with emphasis on the case of a source spectrum that is dominated by several tones, where each is tone specified by its frequency, circumferential mode, and a statistically represented radial mode amplitude distribution. Lining impedance is computed locally by an iterative model imbedded in the FEM propagation code. For propagation in the duct, a rapidly convergent iteration is used in which the defined source spectrum initially determines local lining impedance. In successive iterations the local sound pressure level spectrum on the lining from the previous iteration determines the new local impedance. The iterative model is implemented to assess the attenuation performance of a two degree of freedom lining initially designed with impedance dependent only on the defined source spectrum. The effect of local non-linearity is to reduce realized attenuation in tones targeted in the lining design. In an additional step in the design process, spectrum levels used in the determination of lining parameters to achieve required impedances are adjusted to reflect the reduction of sound pressure level along the lining. This results in a reduction of sensitivity of lining attenuation performance to local non-linearity.