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BUILDING PHYSICS | VIBRATION ANALYSIS

FIGURE 1. Top: Simulated sound pressure in a laboratory with two         explains that the motion of the wall and the sound pressure
chambers divided by a wall. A loudspeaker is placed in the room on       level are the main quantities measured and results show very
the left-hand side. The simulations show that the acoustic resonances    close correlation to the COMSOL Multiphysics model (see
within each room affect the sound insulation. Bottom: Simulated          Figure 2). “The response of the real wall is very clear and the
low-frequency sound originating from outside, around, and inside a       model mimics it almost perfectly. This is the most
building. In both cases, the colors indicate the variation in the sound  spectacular aspect.”
pressure within the rooms and the wall cavities.
                                                                            The model shows that the transmission of sound within
carefully modeled, including the steel frame, the air cavity and         a building is governed by the way in which low-frequency
studs in the wall, the windows, the plywood sheet, and the               waves interact with the fundamental modes of the building
plasterboard. “Each element has a resonance that depends                 components, the dimensions of the room, and the way in
on the wavelength of the sound wave and the pressure                     which air leaks from the building envelope. Vibrations in
distribution. For example, there is high pressure in the speaker         ceilings and walls seem to be the dominant source of
room and lower pressure in the microphone room, and the                  low-frequency indoor sound, with oor vibration driven
resonance of a wall will depend on its length, thickness, and            by sound pressure inside the room.
stiffness,” explains Løvholt.
                                                                         ð CHEAPER AND QUICKER THAN
   The team also had to recognize compound resonances                    PHYSICAL TESTING
created when two components are joined, such as two
pieces of timber that are screwed together. “The advantage               “We now have a tool to predict sound and vibration at low
of COMSOL Multiphysics is that it allows us to enter all the             frequencies,” Løvholt says. “We can use it to design and test
parameters we need to monitor. In particular, it enables us to           mitigation measures such as the lamination of windows and
couple physics, so we can, for example, look at the acoustics            the stiffening of walls — if a wall or window moves less, sound
of open-air sound interacting with indoor structural dynamics.           transfers less. In addition, the model shows us the in uence
The coupling works both ways so we can identify feedback.                small details have on the system; for example, how the screw
This coupling is crucial for our analysis because sound waves            connection between studs and plasterboards can reduce the
can generate a huge range and variety of resonances. The                 effect of a countermeasure, as they actually reduce the overall
model really allows us to see these.”                                    stiffness of the structure.”

   The NGI team then veri ed their simulation with laboratory               The next stage for the team is full-scale eld tests on a real
testing of low-frequency sounds as they were transmitted                 house in an area of Norway that is exposed to aircraft noise.
through a wooden construction with two rooms. Løvholt                    Meanwhile, the team will continue to use and develop the
                                                                         model. “We have never achieved this level of agreement with
                                                                         real-life testing before and it is all down to how we were able
                                                                         to model the different structural elements in
                                                                         COMSOL Multiphysics,” concludes Løvholt. “The model
                                                                         enables us to make decisions and assign countermeasures. This
                                                                         is much cheaper and quicker than physical testing. The model
                                                                         may then be expanded to simulate the sound propagation and

                                                                         vibration in an entire building“ (see Figure 1, bottom). v

                                                                         FIGURE 2. The model accurately captures the location of the
                                                                         resonances as well as the level within a few decibels. As the frequency
                                                                         increases, more modes in smaller and smaller structures will get
                                                                         excited. This shows as the increasing difference between
                                                                         the measurements and the model results.

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