Maria Bayard Dühring - Solid Mechanics

24 Chapter 4 Design of sound barriers by topology optimization [P1]
(a) (b)
Figure 4.2 Results of the optimization for the target frequency f = 125 Hz and β=0.9.
(a): The optimized design where black is solid material and white is air. (b): The distribution
of the sound pressure amplitude around the optimized design.
barriers. The optimized design performs better than the two other barriers in the
entire frequency interval and the T-shaped barrier is better than the straight barrier.
However, Φ is not reduced with as many dB for the single frequencies as in the first
example, but it is decreased with around 2 dB in the entire interval compared to
the straight barrier.
These examples show that the method of topology optimization presented here
is suitable to design sound barriers in outdoor situations for both a single frequency
and a frequency interval. In [P1] it is also shown that Φ can be reduced with up
to 30 dB when a barrier on each side of the source are utilized. In this case the
optimized barriers are displaced compared to each other such that a destructive
wave pattern decreases the objective function. By displacing T-shaped barriers in a
similar way a reduction of almost 10 dB is obtained, which shows that the method
can be employed to find a good position of conventional barriers such that the noise
is reduced. The method is suited for low frequencies, but for frequencies higher than
f = 125 Hz problems start to appear due to the more complicated distribution of
the sound pressure amplitude and because of many local minima.
In the future, the method should be tested for more complicated problem settings
with complex geometries, several sound sources and bigger output areas. In the
outdoor situation sources from several parallel lanes should be included as well as
larger objects along the road. Finally, the described method could be employed to
optimize other acoustic properties such as the reverberation time or the sound power