Maria Bayard Dühring - Solid Mechanics

More documents

Recommendations

Info

570 ARTICLE IN PRESS M.B. <strong>Dühring</strong> et al. / Journal of Sound and Vibration 317 (2008) 557–575 Fig. 11. The geometry for the sound barrier problem in 2D with the design domain Od, the output domain Oop and the point source with the vibrational velocity U. y x 0.1 m 2 m Fig. 12. The dimensions of the barriers with which the performance of the optimized sound barriers will be compared: (a) straight barrier and (b) T-shaped barrier. Table 2 The value of the objective function for the T-shaped barrier and the optimized barrier relative to the straight barrier for each of the two frequencies Frequency f (Hz) Straight F (dB) T-shape DF (dB) Optimized DF (dB) Optimized DF (dB) b ¼ 0:24 b ¼ 0:90 63 68.25 1.70 5.88 7.04 125 70.02 0.90 9.13 a further reduction of the objective function of more than one dB as more reflecting material can be distributed. Note, however, that the amount of material used in the optimized design is well below the limit of 90%. In Fig. 13 the designs for f ¼ 63 Hz with the two different values of b are shown. The two designs are different, but in both cases they look like modified T-shapes and cavities are formed that act as Helmholtz resonators at each side of the barriers. The optimization for the frequency 125 Hz is then done for b ¼ 0:9 and the result can be compared to the result in Ref. [24]. The reduction of the objective function is here 9.13 dB, which is a few dB less than in Ref. [24], but the objective function is here minimized over an entire domain and not only over a few point as in that reference. In Fig. 14 the optimized design for f ¼ 125 Hz is given together with the distribution of the sound pressure amplitude. The design obtained is different from the 0.1 m 0.5 m 0.1 m 2 m
ARTICLE IN PRESS M.B. <strong>Dühring</strong> et al. / Journal of Sound and Vibration 317 (2008) 557–575 571 Fig. 13. The optimized designs for the target frequency f ¼ 63 Hz: (a) with volume fraction b ¼ 0:24 and (b) with volume fraction b ¼ 0:9. Fig. 14. (a) The optimized design for the target frequency f ¼ 125 Hz and b ¼ 0:9 and (b) The distribution of the sound pressure amplitude for the optimized design. design in Ref. [24] with a Helmholtz resonator formed at the edge pointing away from the source where the sound pressure amplitude is high. From these results it is observed that the designs for the two frequencies are very different and the reduction achieved is bigger the higher the frequency is. This tendency is expected,
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 16 and 17:
Page 18 and 19:
Page 20 and 21:
10 Chapter 2 Time-harmonic propagat
Page 22 and 23:
12 Chapter 3 Topology optimization
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
22 Chapter 4 Design of sound barrie
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
28 Chapter 5 Design of photonic-cry
Page 40 and 41:
30 Chapter 5 Design of photonic-cry
Page 42 and 43: 32 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.
Page 74 and 75: 64 References [67] K. Svanberg, “
Page 77: Publication [P1] Acoustic design by
Page 80 and 81: 558 In Ref. [3] it is studied how t
Page 82 and 83: 560 2.2. Design variables and mater
Page 84 and 85: 562 When the mesh size is decreased
Page 86 and 87: 564 objective function, Φ [dB] 130
Page 88 and 89: 566 ARTICLE IN PRESS Fig. 6. The di
Page 90 and 91: 568 ~kðxÞ 1 ¼ k1 ARTICLE IN PRES
Page 94 and 95: 572 ARTICLE IN PRESS M.B. Dühring
Page 96 and 97: 574 frequency or the frequency inte
Page 99: Publication [P2] Design of photonic
Page 102 and 103: photonic-crystal fibers used for me
Page 104 and 105: 2.2 Design variables and material i
Page 106 and 107: two air holes, is Λ = 3.1 µm, the
Page 108 and 109: Figure 4: The geometry of the cente
Page 110 and 111: performance will decrease and some
Page 112 and 113: [23] J. Riishede and O. Sigmund, In
Page 115 and 116: Surface acoustic wave driven light
Page 117 and 118: IDT GaAs AlGaAs 0.10 0.05 0.00 Ampl
Page 119: Publication [P4] Improving the acou
Page 122 and 123: 083529-2 M. B. Dühring and O. Sigm
Page 131: Publication [P5] Design of acousto-
Page 134 and 135: Figure 1: The geometry used in the
Page 136 and 137: where ˜pijkl are the rotated strai
Page 138 and 139: where ∂Φ ∂w R 2,n − i ∂Φ
Page 140 and 141: Figure 3: The distribution of the o
Page 142 and 143:
[12] J.S. Jensen and O. Sigmund, To
Page 145 and 146:
Energy storage and dispersion of su
Page 147 and 148:
093504-3 Dühring, Laude, and Kheli
Page 149 and 150:
093504-5 Dühring, Laude, and Kheli
Page 151:
Publication [P7] Improving surface
Page 154 and 155:
FIG. 1: The geometry of the acousto
Page 156 and 157:
finer mesh. For the coupled model i
Page 158 and 159:
FIG. 4: Results for the finite mode
Page 160 and 161:
FIG. 6: Results for the acousto-opt
Page 162:
Suzuki, A. Onoe, T. Adachi and K. F
show all

Maria Bayard Dühring - Solid Mechanics

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?