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Informationen zum Autor Editors A. Srikantha Phani, University of British Columbia, Canada Mahmoud I. Hussein, University of Colorado Boulder, USA Klappentext * Provides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice* 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 Zusammenfassung * Provides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice* 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 Inhaltsverzeichnis 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 Cauchy-Born 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 Ref...
