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Membrane covered duct lining for high-frequency noise attenuation: Prediction using a Chebyshev collocation method
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Image of FIG. 1.
FIG. 1.

Geometry and domain decomposition for the ChC method. The duct height is and only the lower symmetrical half is solved. The cavity is covered by a membrane and is filled with a sound absorption material of dimensional flow resistivity .

Image of FIG. 2.
FIG. 2.

Comparison of the error for the transmitted wave between the spectral method of ChC and the FD4. The sandwiched segment has , , and . is the number of grids per wavelength.

Image of FIG. 3.
FIG. 3.

Comparison of convergence for three methods for a drumlike silencer with the parameter setting of Eq. (23) and . (a) Energy conservation error for FEM and ChC. (b) Contour of the truncation error of FGa measured in TL relative to the most accurate result calculated by ChC with . (c) The slow FGa convergence with respect to for .

Image of FIG. 4.
FIG. 4.

Comparison of FGa (solid line, ) and ChC solutions (-○-, ) for (a) vertical particle velocity across the duct and for (b) fluid loading along the membrane.

Image of FIG. 5.
FIG. 5.

(a) The capturing of a spectral peak using FGa (dashed lines) of various numbers of modes and ChC with various ranging from 4 (solid line) and 6 (open circles) to 16 (solid line). (b) Vertical acoustic particle velocity distribution in the duct for the peak frequency of 0.126 804 991 with .

Image of FIG. 6.
FIG. 6.

Comparison of (a) accuracy and (b) CPU time performance between ChC and FEM for a dissipative system at high frequency. The parameters are set in Eq. (24).

Image of FIG. 7.
FIG. 7.

Calibration of the DtN boundary condition by comparison with the known solution, Eq. (30), for the higher-order duct acoustics modes. The square domain of size is discretized by Gauss–Lobatto grids.

Image of FIG. 8.
FIG. 8.

Spectral comparison between the optimal membrane covered duct lining with , , and the optimal pure duct lining with .

Image of FIG. 9.
FIG. 9.

Acoustic field for a membrane covered duct lining for the best setting for , , and . (a) SPL distribution in the duct passage. (b) Vertical velocity distribution in the duct (upper) and cavity (lower) regions, joined together by the membrane interface.

Image of FIG. 10.
FIG. 10.

Analysis of the effect of membrane on the lining. (a) Sound intensity across the membrane interface. (b) Plane-wave mode variation with distance. (c) First mode for the half-passage as defined by Eq. (33).


Generic image for table

List of solutions required in the domain decomposition method.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Membrane covered duct lining for high-frequency noise attenuation: Prediction using a Chebyshev collocation method