1. Example: Acoustics in Coupled Rooms

2. Introduction Acoustics in Coupled Rooms
The sound transmission across a building element sample is simulated.
The setup is similar to the one stipulated by the ISO 15186/3 standard as implemented at the Icelandic Building Research Institute (IBRI) in Reykjavik.
This example shows how Extended Multiphysics can be used to split a model into separate exchangeable modules.
In particular, a 2D model of the sample is inserted into the 3D test bench.

3. Geometry Acoustics in Coupled Rooms – Problem Definition
In the 3D geometry, the rooms are modeled as much further apart than they really are.
The rooms are connected via the sample plate, which is modeled in a separate 2D geometry.
Sending room
Receiving room
Sound source
Sample plate

4. Domain Equations – Acoustics
Acoustics in Coupled Rooms – Problem Definition
Domain Equations – Acoustics
Frequency domain acoustics is goverened by a slightly modified Helmholtz’s equation for the acoustic pressure, p.
Material properties are density, r0, and speed of sound, c.
Note that the density cannot be eliminated from the equation unless it is a global constant

5. Domain Equations – Structure
Acoustics in Coupled Rooms – Problem Definition
Domain Equations – Structure
As a simple example, a 1 cm thick, homogenous steel plate is used as sample.
The plate is modeled using plate elements of Reissner-Mindlin type.
The pressure difference between the rooms enter the plate equations as a surface load.

6. Boundary Conditions – Acoustics
Acoustics in Coupled Rooms – Problem Definition
Boundary Conditions – Acoustics
The natural boundary condition corresponds to inward normal acceleration. Three types are used:
Specified normal acceleration,
given by plate movement
Specified impedance, partly
absorbing
Hard wall

7. Boundary Conditions – Structure
Acoustics in Coupled Rooms – Problem Definition
Boundary Conditions – Structure
The plate is mounted in the opening between the rooms using wooden spacers and wedges.
Where the plate is in contact with the spacers, it is considered free to rotate, but not to move.
The rest of the gap between plate and niche wall is filled with a soft sound absorbing material that does not restrict the plate’s movements.

8. Results Acoustics in Coupled Rooms – Results
The instantaneous pressure pattern is shown as isosurfaces.
The wall color represents the sound pressure level in the two rooms (in dB).

9. Results Acoustics in Coupled Rooms – Results
The sound reduction index is not a smooth function of frequency.
This is probably due to the absence of damping in the source room and the sample plate causing pronounced resonance effects.