Maria Bayard Dühring - Solid Mechanics

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Publications The following publications are part of the thesis [P1] M. B. Dühring, J. S. Jensen and O. Sigmund, Acoustic design by topology optimization, Journal of Sound and Vibration, 317, 557-575, 2008. [P2] M. B. Dühring, O. Sigmund and T. Feurer, Design of photonic-bandgap fibers by topology optimization, submitted, 2009. [P3] M. van der Poel, M. Beck, M. B. Dühring, M. M. de Lima, L. H. Frandsen, C. Peucheret, O. Sigmund, U. Jahn, J. M. Hvam and P. V. Santos, Surface acoustic wave driven light modulation, proceedings of the European Conference on Integrated Optics and Technical Exhibition, Copenhagen, Denmark, 25-27 April, 2007. [P4] M. B. Dühring and O. Sigmund, Improving the acousto-optical interaction in a Mach-Zehnder interferometer, Journal of Applied Physics, 105, 083529, 2009. [P5] M. B. Dühring, Design of acousto-optical devices by topology optimization, proceedings of WCSMO-8, 8th World Congress on Structural and Multidisciplinary Optimization, LNEC, Lisbon, Portugal, June 1-5, 2009. [P6] M. B. Dühring, V. Laude and A. Khelif, Energy storage and dispersion of surface acoustic waves trapped in a periodic array of mechanical resonators, Journal of Applied Physics, 105, 093504, 2009. [P7] M. B. Dühring, V. Laude and A. Khelif, Improving surface acousto-optical interaction by high aspect ratio electrodes, submitted, 2009. The paper has received positive review from Journal of Advances in Engineering Software, but in order to reach a broader audience the paper has been withdrawn from this journal and resubmitted to Journal of Applied Physics. iv
Contents Preface i Resumé (in Danish) ii Abstract iii Publications iv Contents v 1 Introduction 1 1.1 Aim of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Time-harmonic propagating waves 3 2.1 Elastic and optical waves . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Elastic waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Optical waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.3 Acousto-optical interaction . . . . . . . . . . . . . . . . . . . . 5 2.2 Modeling of wave problems . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Discretizing and solving wave problems . . . . . . . . . . . . . . . . . 8 3 Topology optimization applied to time-harmonic propagating waves 11 3.1 Topology optimization and propagating waves . . . . . . . . . . . . . 11 3.2 Design variables and material interpolation . . . . . . . . . . . . . . . 14 3.3 The optimization problem . . . . . . . . . . . . . . . . . . . . . . . . 15 3.4 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.5 Practical implementation . . . . . . . . . . . . . . . . . . . . . . . . . 19 4 Design of sound barriers by topology optimization [P1] 21 4.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5 Design of photonic-crystal fibers by topology optimization [P2] 27 5.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 v
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 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 38 and 39: 28 Chapter 5 Design of photonic-cry
Page 44 and 45: 34 Chapter 6 Design of acousto-opti
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48 Chapter 6 Design of acousto-opti
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56 Chapter 7 Concluding remarks des
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58 Chapter 7 Concluding remarks
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60 References [14] E. Yablonovitch,
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62 References [42] A. A. Larsen, B.
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64 References [67] K. Svanberg, “
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Publication [P1] Acoustic design by
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558 In Ref. [3] it is studied how t
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560 2.2. Design variables and mater
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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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