1. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Photograph of the investigated after-treatment device (ATD) together with a drawing of the various parts: (1) flexible inlet; (2) straight pipe; (3) a diverging conical duct; (4) straight pipe; (5) straight pipe; (6) catalytic converter; (7) straight pipe; (8) diesel particulate trap; (9) straight pipe; (10) straight pipe; (11) A converging conical duct; and (12) straight pipe. Geometrical data for all the elements is given in Appendix. Figure Legend:

2. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Approximation of a conical horn using piecewise constant area straight duct sections with constant length Figure Legend:

3. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Cross section of a unit cell in a DPF split into five sections, each described by an acoustic two-port model. Note, the filter section (II) is actually an acoustic four-port but can be reduced to a two-port due to the hard walls in sections I and III. Typical cross dimensions for the quadratic narrow channels in section II are 1–2mm with a wall thickness of 0.3–0.5mm. Figure Legend:

4. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Neighboring channels in a DPF unit. The flow and the acoustic waves enter the channels (1) open upstream and closed downstream, then pass through the porous walls into the channels (2) closed upstream and open downstream. Figure Legend:

5. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Real part of the propagation constants versus normalized shear wave number (sa) for a typical DPF. No flow is assumed, and the filter data are taken from Table and To=293K. °°°, Γ1; —, −Γ2 propagation constants for uncoupled waves and ◇◇◇, propagation constant from Dokumaci. +++, Γ3 and ---, −Γ4 propagation constants for coupled waves. Figure Legend:

6. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Imaginary part of the propagation constants (−Γ) versus normalized shear wave number (sa) for a typical DPF. No flow is assumed, and the filter data are taken from Table at To=293K. °°°, Γ1; —, Γ2 propagation constants for uncoupled waves and ◇◇◇, propagation constant from Dokumaci. +++, Γ3 and ---, Γ4 propagation constants for coupled waves. Figure Legend:

7. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Transmission loss versus frequency at M=0.02 before the inlet of the DPF and Tav=775K. Effect of different acoustic coupling conditions at the inlet and outlet: +++, with energy losses on both sides; —, with the conservation of energy at the inlet and conservation of momentum at the outlet. Figure Legend:

8. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Layout of the test rig for mufflers at MWL/KTH. The two-microphone technique was used for the wave decomposition and to cover the desired frequency range (30–1200Hz); 2 microphone pairs were used. Figure Legend:

9. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Transmission loss versus frequency for the CC at M=0.01 before the inlet and T=293K. ---, simulated using Kirchhoff equation ; —, simulated using Dokumaci ; °°°°, measured. Figure Legend:

10. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Transmission loss versus frequency for the CC at M=0.02 before the inlet and T=293K. ---, simulated using Kirchhoff equation ; —, simulated using Dokumaci ; °°°°, measured. Figure Legend:

11. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Measured and predicted transmission loss for the DPF at M=0.01 before the inlet and T=293K. °°°°, Measured; —, predicted using theory in Sec. ; …, predicted using modified 1D model, Sec.. Figure Legend:

12. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Measured and predicted transmission loss for the DPF at M=0.02 before the inlet and T=293K. °°°°, Measured; —, predicted using theory in Sec. ; …, predicted using modified 1D model, Sec.. Figure Legend:

13. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Transmission loss versus frequency for the ATD at M=0.1 in the inlet pipe and T=293K. —, predicted, °°°°, measured. Figure Legend:

14. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: Modeling and Testing of After-Treatment Devices J. Vib. Acoust. 2005;128(3):347-356. doi:10.1115/1.2172262 Transmission loss versus frequency for the ATD at M=0.15 in the inlet pipe and T=293K. —, predicted, °°°°, measured. Figure Legend: