Maria Bayard Dühring - Solid Mechanics

More documents

Recommendations

Info

2 Chapter 1 Introduction waves. The characteristics of the two wave types are explained and the development in their practical applications during the last century is summarized. It is furthermore explained that the different types of waves can be modeled by time-harmonic second order differential equations, and that they in this work are discretized and solved in a similar way by the finite element method. The concept of topology optimization is introduced in chapter 3 and an overview of the wave propagation problems that have been optimized using this method is presented. In this thesis, the topology optimization method is extended to the three new wave problems. As they can be optimized by the method in the same way with similar expressions for the objective function, the optimization problems are stated on a common form in this chapter together with the corresponding sensitivity analysis. The different approaches to obtain well-defined and mesh-independent designs for the wave problems are summarized. The subsequent three chapters are each concerned with one of the wave propagation problems for which the subject is further explained and results are presented. Chapter 4 deals with the work from publication [P1], which is about acoustic waves propagating in air. A method to design structures by topology optimization in order to minimize noise is presented. The method is demonstrated by two examples where outdoor sound barriers are designed for a single frequency and a frequency interval, respectively. In chapter 5 optical waves propagating in photonic-crystal fibers are considered. Topology optimization is here applied to design the cross section around the hollow core of a holey fiber such that the energy flow through the core is maximized and the overlap with the lossy cladding material is reduced. The chapter is a summary of the work presented in [P2]. The most complicated wave problem of the thesis is presented in chapter 6 where an acousto-optical model is introduced in order to simulate the interaction between surface acoustic waves and optical waves confined in channel waveguides. Both a parameter study of the geometry and topology optimization are employed to optimize the acousto-optical interaction between a Rayleigh wave and optical waves in ridge waveguides. This gives an overview of the results from [P3]-[P5]. The numerical model is furthermore utilized to study the properties of high aspect ratio electrodes, which is work presented in [P6] and [P7]. The acousto-optical interaction between surface acoustic waves generated by these electrodes and an optical wave in a buried waveguide is investigated and compared to results for conventional thin electrodes. Finally, some common conclusions for the project are drawn in chapter 7 and further work is suggested.
Chapter 2 Time-harmonic propagating waves In this chapter elastic and optical waves are introduced and it is explained how they can be modeled by time-harmonic second order differential equations and solved by the finite element method. 2.1 Elastic and optical waves The two wave phenomena known as elastic and electromagnetic waves are studied in this work. They both consist of disturbances that vary in time and space. Elastic waves propagate in a material medium (a fluid or a solid) by displacing material particles from their equilibrium position, which are brought back by restoring forces in the medium. Electromagnetic waves can propagate in both a medium and in vacuum and are composed of an electric and a magnetic field. Despite their different physical origins, elastic and electromagnetic waves have many similarities. They can be described by similar mathematical equations and they both exhibit properties as reflection, diffraction, dispersion, superposition etc. During the last one and a half century the different types of elastic and electromagnetic waves have been studied and methods to model, control and guide them have been developed. This has led to a range of important applications from the early sonar to today’s transport of information by optical fibers as outlined in the following subsections. 2.1.1 Elastic waves Elastic waves propagating in a fluid are referred to as acoustic waves for the lower, audible frequencies and ultrasonic waves for higher frequencies [1]. Because fluids consist of freely-moving particles, there is no shear motion and the waves are only polarized in the longitudinal direction. Their material properties are therefore scalars (as the density and bulk modulus) and the analysis can be done by a scalar equation with a single property (for instance pressure) as the dependent variable. Elastic waves in solid crystals are more complicated and the materials are described by tensors with rank up to four [2, 3]. The waves can have both longitudinal and shear components and must in general be described by vector equations. Bulk waves propagate through the bulk material, whereas surface acoustic waves (SAW) are confined to the material surface with exponential decay into the bulk. Different types of SAWs exist and the most popular is the almost non-dispersive Rayleigh wave, which consists of a longitudinal and a vertical transverse component. The Love wave and the Bleustein-Gulyaev wave are both polarized in the transverse horizontal direction, the first propagates in a thin film on a substrate and the other 3
Page 1: Optimization of acoustic, optical a
Page 4 and 5: Title of the thesis: Optimization o
Page 6 and 7: Resumé (in Danish) Forskningsomr˚
Page 8 and 9: Publications The following publicat
Page 10 and 11: vi Contents 6 Design of acousto-opt
Page 14 and 15: 4 Chapter 2 Time-harmonic propagati
Page 20 and 21: 10 Chapter 2 Time-harmonic propagat
Page 22 and 23: 12 Chapter 3 Topology optimization
Page 32 and 33: 22 Chapter 4 Design of sound barrie
Page 38 and 39: 28 Chapter 5 Design of photonic-cry
Page 44 and 45: 34 Chapter 6 Design of acousto-opti
Page 62 and 63:
52 Chapter 6 Design of acousto-opti
Page 64 and 65:
54 Chapter 6 Design of acousto-opti
Page 66 and 67:
56 Chapter 7 Concluding remarks des
Page 68 and 69:
58 Chapter 7 Concluding remarks
Page 70 and 71:
60 References [14] E. Yablonovitch,
Page 72 and 73:
62 References [42] A. A. Larsen, B.
Page 74 and 75:
64 References [67] K. Svanberg, “
Page 77:
Publication [P1] Acoustic design by
Page 80 and 81:
558 In Ref. [3] it is studied how t
Page 82 and 83:
560 2.2. Design variables and mater
Page 84 and 85:
562 When the mesh size is decreased
Page 86 and 87:
564 objective function, Φ [dB] 130
Page 88 and 89:
566 ARTICLE IN PRESS Fig. 6. The di
Page 90 and 91:
568 ~kðxÞ 1 ¼ k1 ARTICLE IN PRES
Page 92 and 93:
570 ARTICLE IN PRESS M.B. Dühring
Page 94 and 95:
572 ARTICLE IN PRESS M.B. Dühring
Page 96 and 97:
574 frequency or the frequency inte
Page 99:
Publication [P2] Design of photonic
Page 102 and 103:
photonic-crystal fibers used for me
Page 104 and 105:
2.2 Design variables and material i
Page 106 and 107:
two air holes, is Λ = 3.1 µm, the
Page 108 and 109:
Figure 4: The geometry of the cente
Page 110 and 111:
performance will decrease and some
Page 112 and 113:
[23] J. Riishede and O. Sigmund, In
Page 115 and 116:
Surface acoustic wave driven light
Page 117 and 118:
IDT GaAs AlGaAs 0.10 0.05 0.00 Ampl
Page 119:
Publication [P4] Improving the acou
Page 122 and 123:
083529-2 M. B. Dühring and O. Sigm
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 131:
Publication [P5] Design of acousto-
Page 134 and 135:
Figure 1: The geometry used in the
Page 136 and 137:
where ˜pijkl are the rotated strai
Page 138 and 139:
where ∂Φ ∂w R 2,n − i ∂Φ
Page 140 and 141:
Figure 3: The distribution of the o
Page 142 and 143:
[12] J.S. Jensen and O. Sigmund, To
Page 145 and 146:
Energy storage and dispersion of su
Page 147 and 148:
093504-3 Dühring, Laude, and Kheli
Page 149 and 150:
093504-5 Dühring, Laude, and Kheli
Page 151:
Publication [P7] Improving surface
Page 154 and 155:
FIG. 1: The geometry of the acousto
Page 156 and 157:
finer mesh. For the coupled model i
Page 158 and 159:
FIG. 4: Results for the finite mode
Page 160 and 161:
FIG. 6: Results for the acousto-opt
Page 162:
Suzuki, A. Onoe, T. Adachi and K. F
show all

Maria Bayard Dühring - Solid Mechanics

Create successful ePaper yourself

Delete template?

Save as template?