Design Optimisation and Validation of Phononic Crystal Plates for Manipulation of Elastodynamic Guided Waves (eBook)

Supervisor’s Foreword 6
Parts of this thesis have been published in the following documents:JournalsSaeid Hedayatrasa, Mathias Kersemans, Kazem Abhary, Mohammad Uddin and Wim Van Paepegem, ‘Optimisation and experimental validation of stiff porous phononic plates for widest complete bandgap of mixed fundamental guided wave modes’, Mechanical Systems and Signal Processing, Volume 98, Pages 786–801 (January 2018)Saeid Hedayatrasa, Mathias Kersemans, Kazem Abhary, Mohammad Uddin, James K. Guest and Wim Van Paepegem, ‘Maximizing bandgap width and in-plane stiffness of porous phononic plates for tailoring flexural guided waves: topology optimisation and experimental validation’, Mechanics of Materials, Volume 105, Pages 188–203 (February 2017)Saeid Hedayatrasa, Kazem Abhary, Mohammad Uddin and James Guest, ‘Optimal design of tunable phononic bandgap plates under equibiaxial stretch’, Smart Materials and Structures, Volume 25 (5), Pages 05525 (March 2016)Saeid Hedayatrasa, Kazem Abhary, Mohammad Uddin and Ching-Tai Ng, ‘Optimum design of phononic crystal perforated plate structures for widest bandgap of fundamental guided wave modes and maximised in-plane stiffness’, The Mechanics and Physics of Solids, Volume 89, Pages 31–58 (January 2016)Saeid Hedayatrasa, Kazem Abhary and Mohammad Uddin, ‘Numerical study and topology optimisation of 1D periodic bi-material phononic crystal plates for bandgaps of low order Lamb waves’, Ultrasonics, Volume 57, Pages 104–124 (March 2015)ConferencesSaeid Hedayatrasa, Kazem Abhary, Mohammad Uddin, ‘On topology optimisation of acoustic metamaterial lattices for locally resonant bandgaps of flexural waves’, The Second Australasian Acoustical Societies' Conference, Brisbane, Australia, November 2016Saeid Hedayatrasa, Kazem Abhary, Mohammad Uddin and Ching-Tai Ng, ‘Novel Approach in Topology Optimisation of Porous Plate Structures for Phononic Bandgaps of Flexural Waves’, 11th world congress of Structural and Multidisciplinary optimisation, Sydney, Australia, June 2015 8
Journals 8
Conferences 8
Acknowledgements 9
Contents 10
Abbreviations 14
Symbols 15
1 Background and Research Scope 19
1.1 Introduction 19
1.2 Acoustic Metamaterials (AMMs) 20
1.2.1 Phononic Acoustic Bandgaps 20
1.2.2 Locally Resonant Acoustic Bandgaps 22
1.3 Design and Optimisation of (Phononic) Acoustic Bandgaps 23
1.4 Bandgaps of Guided Waves in Plate Structures 25
1.5 Motivation and Research Scope 28
1.6 Concluding Remarks 29
References 30
2 Literature Review and Research Objectives 31
2.1 Introduction 31
2.2 Optimisation of AMMs and Objectives 31
2.2.1 Optimisation of Finite Non-periodic AMM Structure 32
2.2.2 Optimisation of Finite AMM Lattice Structure 34
2.2.3 Optimisation of AMM Unit-Cell Under Perfect Periodicity 35
2.3 PhCrs with Prescribed Shape and Topology 38
2.4 Topology Optimisation of Very Thick 1D PhCrs 39
2.5 Topology Optimisation of Thick 2D PhCrs (Plane-Strain Condition) 41
2.6 Topology Optimisation of PhCr Plates (PhPs) 44
2.7 Tunable PhCrs and Topology Optimisation 46
2.8 The Research Problem and Objectives 48
2.8.1 Optimisation of 1D Bi-Material PhPs and Sensitivity to Unit-Cell’s Filling Fraction and Aspect Ratio 48
2.8.2 Optimisation of Relatively Thin and Thick Porous 2D PhPs for Structurally Worthy Bandgaps of Guided Waves 49
2.8.3 Optimisation of Porous PhPs for Deformation-Induced Tunability 50
2.9 Thesis Structure 50
2.10 Concluding Remarks 52
References 53
3 Optimisation Framework and Fundamental Formulation 57
3.1 Introduction 57
3.2 Optimisation Methods and Genetic Algorithm 57
3.3 Genetic Algorithm Topology Optimisation of PhPs 59
3.3.1 Implemented Multi-objective Optimisation Algorithm (NSGA-II) 60
3.3.2 Topology Mapping and Design Variables 63
3.4 Fundamental Formulation and Modal Band Analysis 66
3.4.1 Elastic Constants and Stress-Strain Relations (Tsai 1992) 66
3.4.2 Navier’s Equation of Equilibrium and FEM Solution 68
3.4.3 The Bloch-Floquet Wave Theory and Unit-Cell’s Modal Band Analysis 69
3.5 Concluding Remarks 72
References 73
4 Optimisation of Bi-material Layered 1D Phononic Crystal Plates (PhPs) 75
4.1 Introduction 75
4.2 Theory and Constitutive Formulation 76
4.2.1 Wave Propagation in 1D Periodic PhP 76
4.2.2 Specialised FEM Model 78
4.2.3 Objective Functions and Optimisation Algorithm 79
4.3 Guided Waves Dispersion and Bandgaps 80
4.4 Topology Optimisation 84
4.4.1 Bandgap Objective-1 87
4.4.2 Bandgap Objective-2 92
4.4.3 Prescribing Definite Symmetric Topology 96
4.5 Frequency Response Analysis of Finite PhP Structures 101
4.6 Concluding Remarks 111
References 112
5 Optimisation of Porous 2D PhPs with Respect to In-Plane Stiffness 113
5.1 Introduction 113
5.2 Theory and Constitutive Formulations 115
5.2.1 Modal Band Analysis of Unit-Cell 115
5.2.2 Objective Functions 118
5.3 Modelling Parameters for FEM Analysis 121
5.3.1 Transversal Mesh Resolution 121
5.3.2 Modelling Void Segments and Compliant Material Properties 122
5.4 NSGA-II Optimisation Algorithm 125
5.5 Topology Optimisation Results 127
5.5.1 Thin PhP with Aspect Ratio 10: Bandgap Objective-1 and Effect of Stress Ratio bs 128
5.5.2 Thin PhP with Aspect Ratio 10: Bandgap Objectives 2 and 3 133
5.5.3 Thick PhP Unit-Cell with Aspect Ratio 2 136
5.6 Frequency Response of Finite PhP Structure 140
5.6.1 Modal Band Structure of Selected Topologies 141
5.6.2 Steady State Frequency Response 141
5.6.3 Transient Frequency Response 145
5.7 Concluding Remarks 149
References 150
6 Optimisation of Porous 2D PhPs: Topology Refinement Study and Other Aspect Ratios 153
6.1 Introduction 153
6.2 Modified Topology Optimisation Strategy 154
6.3 Bandgaps of Asymmetric Guided Wave Modes (Bandgap Objective-1) 156
6.4 Complete Bandgaps of Mixed Guided Waves Modes (Bandgap Objective-3) 161
6.5 Concluding Remarks 165
References 166
7 Optimisation of Porous 2D PhPs for Deformation-Induced Tunability 167
7.1 Introduction 167
7.2 Theory and Governing Equations 170
7.2.1 Nonlinear Static Analysis of Prescribed Finite Strain 171
7.2.2 Hyperelastic Constitutive Model 175
7.2.3 Buckling Stability Analysis 176
7.2.4 Modal Band Analysis 177
7.3 Topology Optimisation Methodology 177
7.3.1 Objective Functions 178
7.3.2 Multi-objective Optimisation Strategy and Algorithm 179
7.3.3 FEM and GA Settings 181
7.4 Optimised Tunable Bandgaps 183
7.4.1 Maximised RBW Gradient 185
7.4.2 Minimised RBW Gradient 189
7.5 Frequency Spectrum of Finite Tunable PhP Lattices 194
7.6 Concluding Remarks 197
References 198
8 Experimental Validation of Optimised Porous 2D PhPs 200
8.1 Introduction 200
8.2 Optimised PhPs for Exclusive Bandgap of Asymmetric Wave Modes 200
8.2.1 Validation of Bandgap of Selected Coarse Topologies 202
8.2.2 Validation of Bandgap of Selected Refined Topologies 207
8.2.3 Validation of Stiffness of Selected Refined Topologies 212
8.3 Optimised PhPs for Complete Bandgap of Mixed Guided Wave Modes 219
8.3.1 Water-Jetted Aluminium PhPs 220
8.3.2 Laser Cut PMMA PhP 226
8.4 Concluding Remarks 233
References 233
9 Conclusions and Recommendations for Future Work 234
9.1 Introduction 234
9.2 Conclusions 235
9.2.1 1D Bi-Material Layered PhPs 235
9.2.2 2D Porous PhPs and In-Plane Stiffness 236
9.2.3 2D Porous PhPs and Deformation-Induced Tunability 237
9.2.4 Experimental Validation of Optimised Porous 2D PhPs 237
9.3 Recommendations for Future Work 239
Curriculum Vitae 240