Example:Acoustics in Coupled Rooms

Introduction

• 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.

Acoustics in Coupled Rooms

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

Domain Equations – Acoustics

• Frequency domain acoustics is goverened by a slightly modified Helmholtz’s equation for the acoustic pressure, p.

• Material properties are density, 0, and speed of sound, c.

• Note that the density cannot be eliminated from the equation unless it is a global constant

Acoustics in Coupled Rooms – Problem Definition

fpc

p

2,0)(

20

2

0

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.

Acoustics in Coupled Rooms – Problem Definition

Specified normal acceleration,given by plate movement

Boundary Conditions – Acoustics

• The natural boundary condition corresponds to inward normal acceleration. Three types are used:

Acoustics in Coupled Rooms – Problem Definition

00

p

n

pZ

ipn

0

ap

n

0

Hard wall

Specified impedance, partly absorbing

Boundary Conditions – Structure

Acoustics in Coupled Rooms – Problem Definition

• 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.

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).

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.