WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

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List of Thesis Papers [1] J. S. Jensen 2003 Journal of Sound and Vibration 266(5), 1053–1078. Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures. [2] J. S. Jensen, O. Sigmund, J. J. Thomsen and M. P. Bendsøe 2002 Design of multi-phase structures with optimized vibrational and wave-transmitting properties. In E. Lund, N. Olhoff and J. Stegmann (eds.), Institute of Mechanical Engineering, Aalborg University, Denmark, 63–66, 15 th Nordic Seminar on Computational Mechanics. [3] B. S. Lazarov and J. S. Jensen 2007 International Journal of Non-Linear Mechanics 42(10), 1186–1193. Low-frequency band gaps in chains with attached non-linear oscillators. [4] O.SigmundandJ.S.Jensen2003PhilosophicalTransactionsof the Royal Society of London Series A-Mathematical Physical and Engineering Sciences 361(1806), 1001–1019. Systematic design of phononic band-gap materials and structures by topology optimization. [5] S. Halkjær, O. Sigmund and J. S. Jensen 2005 Zeitschrift für Kristallographie 220(9–10), 895–905. Inverse design of phononic crystals by topology optimization. [6] J. S. Jensen 2007 Journal of Sound and Vibration 301(1–2), 319–340. Topology optimization problems for reflection and dissipation of elastic waves. [7] J. S. Jensen and N. L. Pedersen 2006 Journal of Sound and Vibration 289(4–5), 967–986. On maximal eigenfrequency separation in two-material structures: the 1D and 2D scalar cases. [8] A. A. Larsen, B. Laksafoss, J. S. Jensen and O. Sigmund 2009 Structural and Multidisciplinary Optimization 37(6), 585–594. Topological material layout in plates for vibration suppression and wave propagation control. [9] J. S.Jensen andO.Sigmund2005Systematic designofacoustic devices by topology optimization. In J. L. Bento Coelho and D. Alarcão (eds.), International Institute of Acoustics and Vibration, 12 th International Congress on Sound and Vibration. [10] J. S. Jensen and O. Sigmund 2004 Applied Physics Letters 84(12), 2022–2024. Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends. iii
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46 Chapter 5 Advanced optimization
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54 Chapter 6 Conclusions
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56 References J. Dahl, J. S. Jensen
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58 References J. Jiang, J. Cai, G.
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60 References defined in two-dimens
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62 References Y. Watanabe, Y. Sugim
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Dansk resumé Dansk titel: Bølger
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Journal of Sound and Vibration 266
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shown for 2-D, as well as for the 1
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ARTICLE IN PRESS J.S. Jensen / Jour
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mj;k .vpþj;qþk ¼ kj;k;3ðvpþj;q
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3. Finite lattice structures ARTICL
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FRF (dB) FRF (dB) 150 100 50 0 ARTI
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4. Conclusions In order to use phon
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Design of multi-phase structures wi
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[dB/1.00 (m/s†)/N] 80 60 40 20 0
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International Journal of Non-Linear
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1188 B.S. Lazarov, J.S. Jensen / In
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10.1098/rsta.2003.1177 r4m THE ROYA
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Phononic band-gap optimization Howe
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Phononic band-gap optimization ^_ _
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Phononic band-gap optimization (aI)
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Phononic band-gap optimization 2, .
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(a) (b) Phononic band-gap optimizat
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0 c , -- -(D ) -c--: (a) free bound
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Phononic band-gap optimization - (a
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Phononic band-gap optimization (a)
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Phoononic band-gap optimization Cox
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896 S. Halkjær, O. Sigmund and J.
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Abstract Journal of Sound and Vibra
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Rðx; tÞ ¼ReðrðxÞe iot Þ¼r r
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for a plane pressure (P) wave of no
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Here, this approach is reused and e
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5.3. FEM discretization and sensiti
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Reflectance, R 1.0 0.8 0.6 0.4 0.2
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Reflectance, R 1.0 0.8 0.6 0.4 0.2
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c Reflectance, R 7.1. Two-phase des
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Dissipation, D 1.0 0.8 0.6 0.4 0.2
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Fig. 14 shows the point-wise dissip
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Acknowledgements The work was parti
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Journal of Sound and Vibration 289
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near the boundaries [11]. The resul
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BeðteÞ ¼ ARTICLE IN PRESS J.S. J
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Design variable, t Design variable,
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Design variable, t Design variable,
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whereas if a is increased material
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For different design parameters the
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ARTICLE IN PRESS J.S. Jensen, N.L.
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ARTICLE IN PRESS J.S. Jensen, N.L.
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the separation of two adjacent eige
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Struct Multidisc Optim DOI 10.1007/
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Topological material layout in plat
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Systematic design of acoustic devic
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ρ=1 κ=1 1 R Figure 1 - A one-dime
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Γ in H design domain ε l symmetry
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objective 0.9 0.8 0.7 0.6 0.5 0.4 0
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APPLIED PHYSICS LETTERS VOLUME 84,
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2024 Appl. Phys. Lett., Vol. 84, No
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1192 J. Opt. Soc. Am. B/Vol. 22, No
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11. W. J. Kim and J. D. O’Brien,
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Normalized transmission 1.0 0.8 0.6
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Loss per bend (dB) 14 12 10 8 6 4 2
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12. P.I. Borel, A. Harpøth, L.H. F
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power flow is evaluated for several
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optimization method has dramaticall
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andwidth of the Y-junction to the b
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JENSEN et al.: TOPOLOGY DESIGN AND
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Imprinted silicon-based nanophotoni
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fabrication method. Furthermore, fa
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In our demonstrations, we have chos
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6 th World Congresses of Structural
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Figure 2: The desired functionality
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The optimization problem in Eq. (4)
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Transmission 1.00 0.95 0.90 0.85 St
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waveguides have inherently lower pr
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INTERNATIONAL JOURNAL FOR NUMERICAL
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TOPOLOGY OPTIMIZATION WITH PADÉ AP
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Response, ln(u 8 u - 8 ) TOPOLOGY O
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Response, ln(u A u - A ) TOPOLOGY O
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which leads to the expressions TOPO
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in which TOPOLOGY OPTIMIZATION WITH
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ENOC-2008, Saint Petersburg, Russia
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We wish to minimize the functional
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Figure 6. Optimized distribution of
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Non-trivial parameter distributions
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706 J.S. Jensen / Comput. Methods A
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Control and Cybernetics vol. 39 (20
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Optimization of space-time material
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