Maria Bayard Dühring - Solid Mechanics

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20 Chapter 3 Topology optimization applied to time-harmonic propagating waves 1. Choose target frequencies ωi and initialize the design variable vector ξ, the counter iter = 0, the tolerance tol=0.01 and change=1. 2. for iter = 1:1000 3. Calculate filtered densities ˜ ξ by the chain rule. 4. Calculate the material values and solve the FE problem based on ˜ ξ. 5. Compute the objective function Ψ and the sensitivities based on ˜ ξ. 6. Calculate filtered sensitivities. 7. Update the design variables ξ new by the MMA-algorithm. 8. Compute change=max(||ξ new -ξ||). 9. If mod(iter,50) == 0 | change < tol, then update target frequencies, the material damping or the filter as appropriate and set change=0.5. 10. Break if change < tol. 11. end 12. Postprocess and display the results. The optimized designs are in general sensitive to the choice of driving frequency or frequency interval as well as other factors such as the volume fraction β, the initial guess and the filter size. It is therefore recommended to choose the driving frequency or the frequency interval carefully and to perform more optimizations with several parameter combinations to obtain the best possible design.
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. 21
Page 1: Optimization of acoustic, optical a
Page 4 and 5: Title of the thesis: Optimization o
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Page 8 and 9: Publications The following publicat
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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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