WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

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Optimization of space-time material layout for 1D wave propagation 613 structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering 71 (2), 197–224. Bendsøe, M.P. and Sigmund, O. (2003) Topology Optimization - Theory, Methods and Applications. Springer-Verlag, Berlin Heidelberg New York. Blekhman, I.I. (2008) Vibrational dynamic materials and composites. Journal of Sound and Vibration 317, 657–663. Blekhman, I.I. and Lurie, K.A. (2000) On dynamic materials. Proceedings of the Russian Academy of Sciences (Doklady) 37, 182–185. Borrvall, T. and Petersson, J. (2001) Topology optimization using regularized intermediate density control. Computer Methods in Applied Mechanics and Engineering 190, 4911–4928. Borrvall, T. and Petersson, J. (2003) Topology optimization of fluids in Stokes flow. International Journal for Numerical Methods in Fluids 41, 77–107. Cox, S.J. and Dobson, D.C. (1999) Maximizing band gaps in twodimensional photonic crystals. SIAM Journal for Applied Mathematics 59 (6), 2108–2120. Dahl, J., Jensen, J.S. and Sigmund, O. (2008) Topology optimization for transient wave propagation problems in one dimension. Structural and Multidisciplinary Optimization 36, 585–595. Jensen, J.S. (2008) Time-space topology optimization. In: B.H.V. Topping and M. Papadrakakis, eds., Proceedings of the Ninth International Conference on Computational Structures Technology. Civil-Comp Press, Stirlingshire, United Kingdom. Paper 72. Jensen, J.S. (2009) Space-time topology optimization for one-dimensional wave propagation. Computer Methods in Applied Mechanics and Engineering 198, 705–715. Krylov, V. and Sorokin, S.V. (1997) Dynamics of elastic beams with controlled distributed stiffness parameters. Smart Materials and Structures 6, 573–582. Lurie, K.A. (1997) Effective properties of smart elastic laminates and the screening phenomenon. International Journal of Solids and Structures 34, 1633–1643. Lurie, K.A. (2006) An Introduction to Mathematical Theory of Dynamic Materials. Springer-Verlag, Berlin Heidelberg New York. Maestre, F., Münch, A. and Pedregal, P. (2007) A spatio-temporal design problem for a damped wave equation. SIAM Journal of Applied Mathematics 68, 109–132. Maestre, F. and Pedregal, P. (2009) Dynamic materials for an optimal design problem under the two-dimensional wave equation. Discrete and Continuous Dynamical Systems - Series A 23, 973–990. Min, S., Kikuchi, N., Park, Y.C., Kim, S. and Chang, S. (1999) Optimal topology design of structures under dynamic loads. Structural Optimization 17, 208–218.
614 J.S. JENSEN Sigmund, O. and Jensen, J.S. (2003) Systematic design of phononic bandgap materials and structures by topology optimization. Philosophical Transactions of the Royal Society London, Series A (Mathematical, Physical and Engineering Sciences) 361, 1001–1019. Sigmund, O. and Petersson, J. (1998) Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, meshdependencies and local minima. Structural Optimization 16, 68–75. Sorokin, S.V., Ershova, O.A. and Grishina, S.V. (2000) The active control of vibrations of composite beams by parametric stiffness modulation. European Journal of Mechanics A - Solids 19, 873–890. Sorokin, S.V. and Grishina, S.V. (2004) Analysis of wave propagation in sandwich beams with parametric stiffness modulation. Journal of Sound and Vibration 271, 1063–1082. Svanberg, K. (1987) The method of moving asymptotes - a new method for structural optimization. International Journal for Numerical Methods in Engineering 24, 359–373. Tortorelli, D.A. and Michaleris, P. (1994) Design sensitivity analysis: overview and review. Inverse Problems in Engineering 1, 71–105. Turteltaub, S. (2005) Optimal non-homogeneous composites for dynamic loading. Structural and Multidisciplinary Optimization 30, 101–112. Wiberg, N.E. and Li, X.D. (1999) Adaptive finite element procedures for linear and non-linear dynamics. International Journal for Numerical Methods in Engineering 46, 1781–1802. Yoon, G.H., Jensen, J.S. and Sigmund, O. (2007) Topology optimization of acoustic-structure interaction using mixed finite elements. International Journal for Numerical Methods in Engineering 70, 1049–1075.
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WAVES AND VIBRATIONS IN INHOMOGENEO
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Denne afhandling er af Danmarks Tek
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List of Thesis Papers [1] J. S. Jen
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Contents Preface i List of Thesis P
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Chapter 1 Introduction This thesis
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eplacemen Phononic and photonic ban
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Optimal material distribution - top
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Chapter 2 The bandgap phenomenon In
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2.1 Band diagram and forced vibrati
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2.3 Experimental demonstration 11 F
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y 2.5 Nonlinearities 13 Response in
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Relations to recent work 15 Amplitu
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Chapter 3 Bandgap structures as opt
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3.1 Vibration-quenching structures
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3.2 Maximizing wave reflection 21 d
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3.4 Maximizing wave dissipation 23
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3.4 Maximizing wave dissipation 25
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3.5 Plate structures 27 a) b) Figur
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3.6 Acoustic design 29 design domai
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Chapter 4 Optimization of photonic
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4.1 Waveguide bends and junctions 3
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4.2 Photonic crystal building block
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4.2 Photonic crystal building block
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4.4 Ridge waveguides 39 w ε =1 ?
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Relations to recent work 41 wave in
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Chapter 5 Advanced optimization pro
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5.1 Padé approximants 45 h 2h A f
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5.3 Space-time topology optimizatio
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5.3 Space-time topology optimizatio
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Relations to recent work 51 Figure
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Chapter 6 Conclusions In the first
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References K. Asakawa, Y. Sugimoto,
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References 57 W. R. Frei, D. A. Tor
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References 59 F. Maestre, A. Münch
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References 61 O. Sigmund, J. S. Jen
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References 63 X. M. Zhou and G. K.
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Dansk resumé 65 i strukturen. En r
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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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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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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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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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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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Page 281 and 282: 5 Results The optimization algorith
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Page 288 and 289: good for low to moderate stiffness
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Page 296: at the Department of Mechanical Eng
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Page 305 and 306: 606 J.S. JENSEN Energy, E a) Energy
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