WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

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Preface The work collected in this thesis has been carried out during my employment at the Technical University of Denmark, Department of Mechanical Engineering in the period from September 2001 to February 2010. I am indebted to my colleague Ole Sigmund for suggesting to me to return to the scientific environment at the University and coming up with the initial idea to the project that started it all. Also I would like to give my sincere thanks to Jon Juel Thomsen who as my PhD-supervisor gave me my scientific upbringing and has continued to influence me through discussions and project cooperations. I would like to thank all the various members of the TopOpt group who has responded to many ideas and come up with many suggestions and comments in group meetings and at informal events. The staff and students at the section for Solid Mechanics have always provided a friendly and relaxed working atmosphere and have done their best to take my mind off scientific issues by engaging in lively conversations and discussions about daily life. Finally, I would like to thank the two girls in my life, Teresa and Jana, for always putting my work in the proper perspective. i Kgs. Lyngby, February 22, 2010 Jakob Søndergaard Jensen
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Page 3: Denne afhandling er af Danmarks Tek
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Page 12 and 13: 2 Chapter 1 Introduction incident w
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Page 16 and 17: 6 Chapter 1 Introduction convert il
Page 18 and 19: 8 Chapter 2 The bandgap phenomenon
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44 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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