- Page 1 and 2: WAVES AND VIBRATIONS IN INHOMOGENEO
- Page 3: Denne afhandling er af Danmarks Tek
- Page 7 and 8: List of Thesis Papers [1] J. S. Jen
- Page 9 and 10: Contents Preface i List of Thesis P
- Page 11 and 12: Chapter 1 Introduction This thesis
- Page 13 and 14: eplacemen Phononic and photonic ban
- Page 15 and 16: Optimal material distribution - top
- Page 17 and 18: Chapter 2 The bandgap phenomenon In
- Page 19 and 20: 2.1 Band diagram and forced vibrati
- Page 21 and 22: 2.3 Experimental demonstration 11 F
- Page 23 and 24: y 2.5 Nonlinearities 13 Response in
- Page 25 and 26: Relations to recent work 15 Amplitu
- Page 27 and 28: Chapter 3 Bandgap structures as opt
- Page 29: 3.1 Vibration-quenching structures
- Page 33 and 34: 3.4 Maximizing wave dissipation 23
- Page 35 and 36: 3.4 Maximizing wave dissipation 25
- Page 37 and 38: 3.5 Plate structures 27 a) b) Figur
- Page 39 and 40: 3.6 Acoustic design 29 design domai
- Page 41 and 42: Chapter 4 Optimization of photonic
- Page 43 and 44: 4.1 Waveguide bends and junctions 3
- Page 45 and 46: 4.2 Photonic crystal building block
- Page 47 and 48: 4.2 Photonic crystal building block
- Page 49 and 50: 4.4 Ridge waveguides 39 w ε =1 ?
- Page 51 and 52: Relations to recent work 41 wave in
- Page 53 and 54: Chapter 5 Advanced optimization pro
- Page 55 and 56: 5.1 Padé approximants 45 h 2h A f
- Page 57 and 58: 5.3 Space-time topology optimizatio
- Page 59 and 60: 5.3 Space-time topology optimizatio
- Page 61 and 62: Relations to recent work 51 Figure
- Page 63 and 64: Chapter 6 Conclusions In the first
- Page 65 and 66: References K. Asakawa, Y. Sugimoto,
- Page 67 and 68: References 57 W. R. Frei, D. A. Tor
- Page 69 and 70: References 59 F. Maestre, A. Münch
- Page 71 and 72: References 61 O. Sigmund, J. S. Jen
- Page 73 and 74: References 63 X. M. Zhou and G. K.
- Page 75 and 76: Dansk resumé 65 i strukturen. En r
- Page 77 and 78: 1054 ARTICLE IN PRESS J.S. Jensen /
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1058 fundamental eigenfrequency o
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1060 ðo 2 y;j;k ARTICLE IN PRESS J
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1062 local resonator and splits up
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1064 3.1. Model equations A finite
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1066 FRF (dB) 150 100 50 0 -50 -100
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1068 3.3. Example 2: a 2-D waveguid
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1070 ARTICLE IN PRESS J.S. Jensen /
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1072 ARTICLE IN PRESS J.S. Jensen /
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1074 ARTICLE IN PRESS J.S. Jensen /
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1076 ARTICLE IN PRESS J.S. Jensen /
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1078 ARTICLE IN PRESS J.S. Jensen /
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wave-guiding properties show promis
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(a) (b) Acceleration response (dB)
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B.S. Lazarov, J.S. Jensen / Interna
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ω/κ ω/κ 1.5 1.4 1.3 1.2 1.1 1 0
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[B 2000 ] [B 2000 ] [B 2000 ] 0.25
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[B 400 ] 0.25 0.2 0.15 0.1 0.05 B.S
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1002 (a) (c) (e) 0. Sigmund and J.
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1004 O. Sigmund and J. S. Jensen wh
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1006 (a) - - - - - - _ - - - - I I
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1008 O. Sigmund and J. S. Jensen we
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1010 O. Sigmund and J. S. Jensen Th
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1012 (a) (b) O. Sigmund and J. S. J
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1014 . ct . _ a) Q^ s^c "3
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1016 O. Sigmund and J. S. Jensen (a
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1018 O. Sigmund and J. S. Jensen 4.
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Z. Kristallogr. 220 (2005) 895-905
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Inverse design of phononic crystals
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Inverse design of phononic crystals
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Inverse design of phononic crystals
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Inverse design of phononic crystals
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Inverse design of phononic crystals
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320 Optimization of the dissipation
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322 The reflection of the wave is f
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324 which averaged over a wave peri
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326 where the modified stress compo
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328 optimization algorithm is enhan
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330 reflectance are also seen (Fig.
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332 It should be emphasized that ot
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334 b Dissipation, D c Dissipation,
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336 7.2. Three-phase design ARTICLE
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338 ARTICLE IN PRESS J.S. Jensen /
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340 ARTICLE IN PRESS J.S. Jensen /
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968 ARTICLE IN PRESS J.S. Jensen, N
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970 To solve the wave equation with
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972 In the following section, we sh
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974 Design variable, t Design varia
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976 Eigenvalue ratio, ω n+1 2 /ωn
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978 to a design parameter te are gi
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980 ARTICLE IN PRESS J.S. Jensen, N
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982 respect to the higher bound C1
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984 instead vary the value of b. Th
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986 References ARTICLE IN PRESS J.S
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a thick solid was considered. A few
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The above expressions provide insta
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In all the examples shown a density
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domain. To the very left the passiv
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Jensen JS, Sigmund O (2005) Topolog
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paper extends on this work. For an
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R 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
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objective 1 0.9 0.8 0.7 0.6 0.5 0.4
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The optimization algorithm employs
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Appl. Phys. Lett., Vol. 84, No. 12,
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J. S. Jensen and O. Sigmund Vol. 22
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J. S. Jensen and O. Sigmund Vol. 22
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J. S. Jensen and O. Sigmund Vol. 22
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J. S. Jensen and O. Sigmund Vol. 22
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Topology optimization and fabricati
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Normalized transmission 1.0 0.8 0.6
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Fig. 4. Scanning electron micrograp
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Broadband photonic crystal waveguid
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2. Design and fabrication Silicon-o
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Fig. 3. Steady-state magnetic field
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Topology optimised broadband photon
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1202 IEEE PHOTONICS TECHNOLOGY LETT
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1204 IEEE PHOTONICS TECHNOLOGY LETT
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11. P. Debackere, S. Scheerlinck, P
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nanoimprinted patterns are transfer
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emoved and the spectra changed dras
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Y-splitter W1 waveguide 60-degree b
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5. Photonic Wire Waveguides Figure
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Figure 5: Optimized designs and cor
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Figure 8: Optimized designs and cor
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[13] Borel P I, Frandsen L H, Harp
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1606 J. S. JENSEN To compute a freq
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1608 J. S. JENSEN Cramer’s rule [
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1610 J. S. JENSEN The following pro
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1612 J. S. JENSEN Table I. Coeffici
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1614 J. S. JENSEN h 2h Α fcos Ωt
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1616 J. S. JENSEN The derivative of
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1618 J. S. JENSEN which is solved f
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1620 J. S. JENSEN Based on the expr
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1622 J. S. JENSEN Response, ln(u ti
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1624 J. S. JENSEN h 2h fcos Ωt Fi
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1626 J. S. JENSEN details and have
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1628 J. S. JENSEN Equation (A10) co
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1630 J. S. JENSEN 7. Coyette J-P, L
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The number of masses in the chain t
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5 Results The optimization algorith
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Figure 9. Response for optimized de
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Space-time topology optimization fo
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good for low to moderate stiffness
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V ¼ 0:3 at a given time instant fo
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The parameters used in this example
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Normalized amplitude 1 0.9 0.8 0.7
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at the Department of Mechanical Eng
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600 J.S. JENSEN techniques for obta
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602 J.S. JENSEN 1 and 2, where the
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604 J.S. JENSEN 4. Numerical analys
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606 J.S. JENSEN Energy, E a) Energy
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608 J.S. JENSEN relaxed somewhat in
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610 J.S. JENSEN when the contrast i
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612 J.S. JENSEN 6. Summary and conc
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614 J.S. JENSEN Sigmund, O. and Jen