1. Absorptive Muffler with Shells
Acoustics Model Gallery # 14717

2. Background and Motivation
This model presents an extension of the Absorptive Muffler model located in the model library, by including acoustic-solid interactions.
The muffler structure is modeled using shells elements.
The coupled problem us set up using the Acoustic-Shell Interaction, Frequency Domain user interface.
This model analyzed the effects elastic vibrations in the solid muffler structure will have on the transmission loss (TL). The results are compared to a pure acoustics model and an eigenfrequency analysis of the pure structural problem.
In real muffler systems the main effect of acoustic-structure interaction is probably due to elastic vibrations sources that stem from vibrations in in the full exhaust system. In this model the vibrations are induced by the pressure waves in the air.
Adding structural sources can also be done by specifying a deformation or a velocity on edges or points in the structure.

3. Geometry and Operating Conditions
Outlet: Plane wave radiation
Muffler made of 0.5 mm steel plates
Fixed constraint
Fixing straps made of 2 mm steel
Inlet: Plane wave radiation and incident field

4. Modeling Interfaces
The model sets up and solves three physics interfaces:
Pressure Acoustics to solve the model with pure acoustics (same as the Absorptive Muffler model)
Acoustic-Shell Interaction to solve the coupled acoustic and solid vibrations problem
Shell to determine the pure structural eigenmodes of the muffler system

5. Modeling Interfaces: Pressure Acoustics
Absorbing liner

6. Modeling Interfaces: Acoustic-Shell
Select the shells using a selection created under the Definitions node.
Add some isotropic damping to the model.

7. Modeling Interfaces: Acoustic-Shell
Change the thickness of the shell where the fixing strap is located.
In this model the inlet/outlet pipes are fixed at the ends. Here it would be possible to add vibration sources that stem from vibrations in the rest of the exhaust system.

8. Modeling Interfaces: Shell
Set up the pure shell model in the same way as it was set up for the Acoustic-Shell multiphysics interface.

9. Mesh
Set up two meshes, one for the problem involving acoustics and one for the pure structural problem. In the latter case only map the shell surface.

10. Solve
Set up three studies, one for the pure acoustic problem, one for the acoustic-shell problem, and one for the eigenfrequency analysis of the pure shell problem.
Select the physics to solve in the “Solve for” column.

11. Results: Pure Acoustic
Plot the sound pressure level, the pressure distribution and much more using surface plots, isosurfaces or cross section plots. See the Absorprtive Muffler for more information.

12. Results: Transmission Loss
In the low frequency range the modes are symmetric and easy to excite by the incident symmetric pressure field.

13. Results: Eigenmodes 206 Hz Some mode shapes located around 150 Hz.

14. Concluding Remarks
The interaction is strong in the low frequency range where the eigenmodes are symmetric and easily excited by the acoustic field. The field will not excite all existing eigenmodes.
There is probably a stronger effects on the transmission loss if there are structural vibrations sources; these can result in a transmission loss that is negative. Strong acoustic sources may appear at the muffler walls, these are not accounted for in the “input” power which is pure acoustic.
Even though the effect of the pressure-solid interaction is not large, undesired eigenmodes of the muffler structure may exist in places where large transmission loss is desired