WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

Contents
Preface i
List of Thesis Papers iii
Contents v
1 Introduction 1
2 The bandgap phenomenon 7
2.1 Band diagram and forced vibrations . . . . . . . . . . . . . . . . . . . 8
2.2 Structural damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Experimental demonstration . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Low-frequency bandgaps . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Bandgap structures as optimal designs 17
3.1 Vibration-quenching structures . . . . . . . . . . . . . . . . . . . . . 18
3.2 Maximizing wave reflection . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Eigenfrequency separation . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4 Maximizing wave dissipation . . . . . . . . . . . . . . . . . . . . . . . 23
3.5 Plate structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.6 Acoustic design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4 Optimization of photonic waveguides 31
4.1 Waveguide bends and junctions . . . . . . . . . . . . . . . . . . . . . 32
4.2 Photonic crystal building blocks . . . . . . . . . . . . . . . . . . . . . 35
4.3 Advanced functionalities . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.4 Ridge waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5 Advanced optimization procedures 43
5.1 Padé approximants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.2 Nonlinear transients . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.3 Space-time topology optimization . . . . . . . . . . . . . . . . . . . . 47
6 Conclusions 53
References 54
v