WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

Chapter 6
Conclusions
In the first five chapter of this thesis the main findings of papers [1]–[21] are summarized.
Chapter 2 contains contributions to the basic understanding of the bandgap
phenomenon, exemplified in simple one- and two-dimensional mass-spring structures.
Chapter 3 demonstrates how the method of topology optimization can be
applied to design various elastic and acoustic bandgap structures. Chapter 4 extends
the topology optimization method to deal with photonic waveguide components
and in Chapter 5 three advanced optimization methods and algorithms for
the optimization of dynamical systems are presented.
The main contributions of this thesis are:
• Analysis of the connection between the band diagram for a periodic material
andtheforcedvibrationresponseforafinitestructuremadefromthismaterial.
• Analysis of the effect of nonlinearities on the bandgap effect of a mass-spring
system with attached oscillators.
• Design of phononic bandgap structures using a material layout optimization
method.
• Design of key components of photonic crystal waveguides using topology optimization.
• Development of new techniques based on artificial damping for using topology
optimization to design bandgap structures
• Design of acoustic structures using topology optimization.
• Development of an efficient methodology for optimizing the performance of
dynamic system using Padé approximants.
• Topology optimization for transient wave propagation problems with nonlinearities.
• Development of a space-time topology optimization formulation to design
structures with optimized material distributions that can vary in time.
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