Maria Bayard Dühring - Solid Mechanics

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.