Maria Bayard Dühring - Solid Mechanics

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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
4.2 Results 25 objective function, Φ [dB] (a) (b) 72 70 68 66 64 62 straight barrier T−barrier optimized design frequency borders 60 60 70 80 90 100 110 120 frequency, f [Hz] Figure 4.3 Results of the optimization for the frequency interval [63;125] Hz with 7 target frequencies and β = 0.9. (a): The optimized design where black indicates solid material and white is air. (b): The value of Φ as function of the frequency f for the straight, T-shaped and optimized sound barriers. into an area or through an opening between coupled rooms.
Page 1: Optimization of acoustic, optical a
Page 4 and 5: Title of the thesis: Optimization o
Page 6 and 7: Resumé (in Danish) Forskningsomr˚
Page 8 and 9: Publications The following publicat
Page 10 and 11: vi Contents 6 Design of acousto-opt
Page 12 and 13: 2 Chapter 1 Introduction waves. The
Page 14 and 15: 4 Chapter 2 Time-harmonic propagati
Page 20 and 21: 10 Chapter 2 Time-harmonic propagat
Page 22 and 23: 12 Chapter 3 Topology optimization
Page 32 and 33: 22 Chapter 4 Design of sound barrie
Page 36 and 37: 26 Chapter 4 Design of sound barrie
Page 38 and 39: 28 Chapter 5 Design of photonic-cry
Page 44 and 45: 34 Chapter 6 Design of acousto-opti
Page 66 and 67: 56 Chapter 7 Concluding remarks des
Page 68 and 69: 58 Chapter 7 Concluding remarks
Page 70 and 71: 60 References [14] E. Yablonovitch,
Page 72 and 73: 62 References [42] A. A. Larsen, B.
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562 When the mesh size is decreased
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564 objective function, Φ [dB] 130
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566 ARTICLE IN PRESS Fig. 6. The di
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568 ~kðxÞ 1 ¼ k1 ARTICLE IN PRES
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570 ARTICLE IN PRESS M.B. Dühring
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572 ARTICLE IN PRESS M.B. Dühring
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574 frequency or the frequency inte
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Publication [P2] Design of photonic
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photonic-crystal fibers used for me
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2.2 Design variables and material i
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two air holes, is Λ = 3.1 µm, the
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Figure 4: The geometry of the cente
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performance will decrease and some
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[23] J. Riishede and O. Sigmund, In
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Surface acoustic wave driven light
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IDT GaAs AlGaAs 0.10 0.05 0.00 Ampl
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Publication [P4] Improving the acou
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083529-2 M. B. Dühring and O. Sigm
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Publication [P5] Design of acousto-
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Figure 1: The geometry used in the
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where ˜pijkl are the rotated strai
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where ∂Φ ∂w R 2,n − i ∂Φ
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Figure 3: The distribution of the o
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[12] J.S. Jensen and O. Sigmund, To
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Energy storage and dispersion of su
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093504-3 Dühring, Laude, and Kheli
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093504-5 Dühring, Laude, and Kheli
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Publication [P7] Improving surface
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FIG. 1: The geometry of the acousto
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finer mesh. For the coupled model i
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FIG. 4: Results for the finite mode
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FIG. 6: Results for the acousto-opt
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Suzuki, A. Onoe, T. Adachi and K. F
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Maria Bayard Dühring - Solid Mechanics

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