Maria Bayard Dühring - Solid Mechanics

Chapter 4
Design of sound barriers by topology optimization
[P1]
The first type of wave problem considered in the present work, is the propagation
of acoustic waves in air, where topology optimization is employed to optimize the
distribution of materials in structures to reduce noise. This chapter is a summary
of the work presented in publication [P1].
It is essential to control acoustic properties in a wide range of problems such as in
the design of loudspeakers, the layout of rooms for good speech conditions or in noise
reduction where sound waves can have a damaging effect on humans or electronic
equipment. Reduction of sound is important for indoor situations as in open offices,
staircases as well as in car and airplane cabins or for outdoor problems, for instance
along roads with heavy traffic. The most common way to reduce noise is by passive
noise control where structures as sound barriers are employed to screen from the
sound or where absorbers as resonators, porous absorbing material or membranes
are used to absorb the acoustic waves. Both experimental and theoretical work has
been employed in order to design for noise reduction. Scale models of sound barriers
with different shapes are for instance investigated in [69, 70], and numerical results
for sound barriers are obtained with a boundary element method in [71, 72]. In
both cases the T-shaped barrier tends to give the largest noise reduction. Different
kinds of optimization methods have been applied to acoustic problems as shape
optimization, see [73], and in [48] a systematic way to design barriers with genetic
algorithms is suggested. Lately, topology optimization has been applied to control
sound by different structures such as acoustic horns, plate and shell structures or
reflection champers as outlined in section 3.1.
In [P1] the method of topology optimization is extended to problems were noise
is reduced by passive noise control for a single driving frequency or a frequency
interval for 2D and 3D problems. It is first applied to room acoustics where the
structure of the ceiling is optimized in order to reduce the sound in a certain part of
the room. This concept was first presented by the author in [74] and extended with
more examples in [P1]. The objective function is minimized because of the forming
of cavities acting as Helmholtz resonators, or by moving natural frequencies, that
are close to the diving frequency, to lower or higher values by redistributing material
at the nodal planes or at the high pressure amplitudes, respectively. It is also shown
that the method is suitable to find optimized distributions of absorbing material
along the walls. Finally, the method is applied to design outdoor sound barriers
and two examples for a single frequency and a frequency interval, respectively, are
presented in the following to show the performance of the method.
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