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Offers comprehensive treatment of dynamics of lattice materials and periodic materials in general, including phononic crystals and elastic metamaterials
Provides an in depth introduction to elastostatics and elastodynamics of lattice materials
Covers advanced topics such as damping, nonlinearity, instability, impact and nanoscale systems
Introduces contemporary concepts including pentamodes, local resonance and inertial amplification
Includes chapters on fast computation and design optimization tools
Topics are introduced using simple systems and generalized to more complex structures with a focus on dispersion characteristics
Auteur
Editors
A. Srikantha Phani, University of British Columbia, Canada
Mahmoud I. Hussein, University of Colorado Boulder, USA
Contenu
List of Contributors xiii
Foreword xv
Preface xxv
**1 Introduction to Lattice Materials 1
**A. Srikantha Phani andMahmoud I. Hussein
1.1 Introduction 1
1.2 Lattice Materials and Structures 2
1.2.1 Material versus Structure 3
1.2.2 Motivation 3
1.2.3 Classification of Lattices and Maxwell's Rule 4
1.2.4 ManufacturingMethods 6
1.2.5 Applications 7
1.3 Overview of Chapters 8
Acknowledgment 10
References 10
**2 Elastostatics of Lattice Materials 19
**D. Pasini and S. Arabnejad
2.1 Introduction 19
2.2 The RVE 21
2.3 Surface Average Approach 22
2.4 Volume Average Approach 25
2.5 Force-based Approach 25
2.6 Asymptotic Homogenization Method 26
2.7 Generalized Continuum Theory 29
2.8 Homogenization via BlochWave Analysis and the CauchyBorn Hypothesis 32
2.9 Multiscale Matrix-based Computational Technique 34
2.10 Homogenization based on the Equation of Motion 36
2.11 Case Study: Property Predictions for a Hexagonal Lattice 38
2.12 Conclusions 42
References 43
**3 Elastodynamics of Lattice Materials 53
**A. Srikantha Phani
3.1 Introduction 53
3.2 One-dimensional Lattices 55
3.2.1 Bloch's Theorem 57
3.2.2 Application of Bloch's Theorem 59
3.2.3 Dispersion Curves and Unit-cell Resonances 59
3.2.4 Continuous Lattices: Local Resonance and sub-Bragg Band Gaps 61
3.2.5 Dispersion Curves of a Beam Lattice 62
3.2.6 Receptance Method 64
3.2.7 Synopsis of 1D Lattices 67
3.3 Two-dimensional Lattice Materials 67
3.3.1 Application of Bloch's Theorem to 2D Lattices 67
3.3.2 Discrete Square Lattice 70
3.4 Lattice Materials 72
3.4.1 Finite Element Modelling of the Unit Cell 75
3.4.2 Band Structure of Lattice Topologies 77
3.4.3 Directionality ofWave Propagation 84
3.5 Tunneling and EvanescentWaves 85
3.6 Concluding Remarks 87
3.7 Acknowledgments 87
References 87
**4 Wave Propagation in Damped Lattice Materials 93
**Dimitri Krattiger, A. Srikantha Phani andMahmoud I. Hussein
4.1 Introduction 93
4.2 One-dimensionalMassSpringDamperModel 95
4.2.1 1D Model Description 95
4.2.2 Free-wave Solution 96
State-spaceWave Calculation 97
BlochRayleigh Perturbation Method 97
4.2.3 Driven-wave Solution 98
4.2.4 1D Damped Band Structures 98
4.3 Two-dimensional PlatePlate Lattice Model 99
4.3.1 2D Model Description 99
4.3.2 Extension of Driven-wave Calculations to 2D Domains 100
4.3.3 2D Damped Band Structures 101
References 104
**5 Wave Propagation in Nonlinear Lattice Materials 107
**Kevin L.Manktelow,Massimo Ruzzene andMichael J. Leamy
5.1 Overview 107
5.2 Weakly Nonlinear Dispersion Analysis 108
5.3 Application to a 1D Monoatomic Chain 114
5.3.1 Overview 114
5.3.2 Model Description and Nonlinear Governing Equation 114
5.3.3 Single-wave Dispersion Analysis 115
5.3.4 Multi-wave Dispersion Analysis 116
Case 1. GeneralWaveWave Interactions 117
Case 2. Long-wavelength LimitWaveWave Interactions 119
5.3.5 Numerical Verification and Discussion 122
5.4 Application to a 2D Monoatomic Lattice 123
5.4.1 Overview 123
5.4.2 Model Description and Nonlinear Governing Equation 124
5.4.3 Multiple-scale Perturbation Analysis 125
5.4.4 Analysis of Predicted Dispersion Shifts 127
5.4.5 Numerical Simulation Validation Cases 129
Analysis Method 130
Orthogonal and Oblique Interaction 131 5.4.6 Applicati...