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英文全書下載 Viscoelastic Materials. Roderic Lakes 2009 《粘彈性材料》
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陳小黑
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2015-1-9 22:34
標(biāo)題:
英文全書下載 Viscoelastic Materials. Roderic Lakes 2009 《粘彈性材料》
本帖最后由 陳小黑 于 2015-1-9 22:37 編輯
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目錄
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Contents
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Preface page xvii
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1 Introduction: Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
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1.1 Viscoelastic Phenomena 1
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1.2 Motivations for Studying Viscoelasticity 3
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1.3 Transient Properties: Creep and Relaxation 3
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1.3.1 Viscoelastic Functions J (t), E(t) 3
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1.3.2 Solids and Liquids 7
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1.4 Dynamic Response to Sinusoidal Load: E∗, tanδ 8
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1.5 Demonstration of Viscoelastic Behavior 10
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1.6 Historical Aspects 10
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1.7 Summary 11
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1.8 Examples 11
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1.9 Problems 12
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Bibliography 12
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2 Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
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2.1 Introduction 14
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2.2 Prediction of the Response of Linearly Viscoelastic Materials 14
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2.2.1 Prediction of Recovery from Relaxation E(t) 14
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2.2.2 Prediction of Response to Arbitrary Strain History 15
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2.3 Restrictions on the Viscoelastic Functions 17
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2.3.1 Roles of Energy and Passivity 17
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2.3.2 Fading Memory 18
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2.4 Relation between Creep and Relaxation 19
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2.4.1 Analysis by Laplace Transforms: J (t) ↔ E(t) 19
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2.4.2 Analysis by Direct Construction: J (t) ↔ E(t) 20
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2.5 Stress versus Strain for Constant Strain Rate 20
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2.6 Particular Creep and Relaxation Functions 21
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2.6.1 Exponentials and Mechanical Models 21
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2.6.2 Exponentials and Internal Causal Variables 26
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2.6.3 Fractional Derivatives 27
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2.6.4 Power-Law Behavior 28
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2.6.5 Stretched Exponential 29
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2.6.6 Logarithmic Creep; Kuhn Model 29
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2.6.7 Distinguishing among Viscoelastic Functions 30
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2.7 Effect of Temperature 30
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2.8 Three-Dimensional Linear Constitutive Equation 33
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2.9 Aging Materials 35
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2.10 Dielectric and Other Forms of Relaxation 35
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2.11 Adaptive and “Smart” Materials 36
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2.12 Effect of Nonlinearity 37
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2.12.1 Constitutive Equations 37
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2.12.2 Creep–Relaxation Interrelation: Nonlinear 40
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2.13 Summary 43
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2.14 Examples 43
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2.15 Problems 51
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Bibliography 52
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3 Dynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
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3.1 Introduction and Rationale 55
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3.2 The Linear Dynamic Response Functions E∗, tanδ 56
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3.2.1 Response to Sinusoidal Input 57
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3.2.2 Dynamic Stress–Strain Relation 59
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3.2.3 Standard Linear Solid 62
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3.3 Kramers–Kronig Relations 63
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3.4 Energy Storage and Dissipation 65
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3.5 Resonance of Structural Members 67
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3.5.1 Resonance, Lumped System 67
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3.5.2 Resonance, Distributed System 71
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3.6 Decay of Resonant Vibration 74
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3.7 Wave Propagation and Attenuation 77
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3.8 Measures of Damping 79
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3.9 Nonlinear Materials 79
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3.10 Summary 81
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3.11 Examples 81
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3.12 Problems 88
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Bibliography 89
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4 Conceptual Structure of Linear Viscoelasticity . . . . . . . . . . . . . . . 91
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4.1 Introduction 91
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4.2 Spectra in Linear Viscoelasticity 92
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4.2.1 Definitions H(τ ), L(τ ) and Exact Interrelations 92
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4.2.2 Particular Spectra 93
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4.3 Approximate Interrelations of Viscoelastic Functions 95
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4.3.1 Interrelations Involving the Spectra 95
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4.3.2 Interrelations Involving Measurable Functions 98
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4.3.3 Summary, Approximate Relations 101
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4.4 Conceptual Organization of the Viscoelastic Functions 101
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4.5 Summary 104
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4.6 Examples 104
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4.7 Problems 109
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Bibliography 109
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5 Viscoelastic Stress and Deformation Analysis . . . . . . . . . . . . . . . 111
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5.1 Introduction 111
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5.2 Three-Dimensional Constitutive Equation 111
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5.3 Pure Bending by Direct Construction 112
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5.4 Correspondence Principle 114
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5.5 Pure Bending by Correspondence 116
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5.6 Correspondence Principle in Three Dimensions 116
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5.6.1 Constitutive Equations 116
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5.6.2 Rigid Indenter on a Semi-Infinite Solid 117
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5.6.3 Viscoelastic Rod Held at Constant Extension 119
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5.6.4 Stress Concentration 119
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5.6.5 Saint Venant’s Principle 120
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5.7 Poisson’s Ratio ν(t) 121
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5.7.1 Relaxation in Tension 121
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5.7.2 Creep in Tension 123
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5.8 Dynamic Problems: Effects of Inertia 124
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5.8.1 Longitudinal Vibration and Waves in a Rod 124
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5.8.2 Torsional Waves and Vibration in a Rod 125
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5.8.3 Bending Waves and Vibration 128
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5.8.4 Waves in Three Dimensions 129
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5.9 Noncorrespondence Problems 131
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5.9.1 Solution by Direct Construction: Example 131
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5.9.2 A Generalized Correspondence Principle 132
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5.9.3 Contact Problems 132
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5.10 Bending in Nonlinear Viscoelasticity 133
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5.11 Summary 134
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5.12 Examples 134
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5.13 Problems 142
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Bibliography 142
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6 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
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6.1 Introduction and General Requirements 145
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6.2 Creep 146
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6.2.1 Creep: Simple Methods to Obtain J (t) 146
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6.2.2 Effect of Risetime in Transient Tests 146
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6.2.3 Creep in Anisotropic Media 148
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6.2.4 Creep in Nonlinear Media 148
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6.3 Inference of Moduli 150
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6.3.1 Use of Analytical Solutions 150
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6.3.2 Compression of a Block 151
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6.4 Displacement and Strain Measurement 152
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6.5 Force Measurement 156
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6.6 Load Application 157
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6.7 Environmental Control 157
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6.8 Subresonant Dynamic Methods 158
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6.8.1 Phase Determination 158
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6.8.2 Nonlinear Materials 160
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6.8.3 Rebound Test 161
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6.9 Resonance Methods 161
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6.9.1 General Principles 161
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6.9.2 Particular Resonance Methods 163
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6.9.3 Methods for Low-Loss or High-Loss Materials 166
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6.9.4 Resonant Ultrasound Spectroscopy 168
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6.10 Achieving a Wide Range of Time or Frequency 171
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6.10.1 Rationale 171
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6.10.2 Multiple Instruments and Long Creep 172
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6.10.3 Time–Temperature Superposition 172
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6.11 Test Instruments for Viscoelasticity 173
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6.11.1 Servohydraulic Test Machines 173
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6.11.2A Relaxation Instrument 174
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6.11.3 Driven Torsion Pendulum Devices 174
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6.11.4 Commercial Viscoelastic Instrumentation 178
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6.11.5 Instruments for a Wide Range of Time and Frequency 179
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6.11.6 Fluctuation–Dissipation Relation 182
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6.11.7 Mapping Properties by Indentation 183
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6.12 Wave Methods 184
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6.13 Summary 188
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6.14 Examples 188
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6.15 Problems 200
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Bibliography 201
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7 Viscoelastic Properties of Materials . . . . . . . . . . . . . . . . . . . . . 207
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7.1 Introduction 207
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7.1.1 Rationale 207
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7.1.2 Overview: Some Common Materials 207
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7.2 Polymers 208
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7.2.1 Shear and Extension in Amorphous Polymers 208
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7.2.2 Bulk Relaxation in Amorphous Polymers 212
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7.2.3 Crystalline Polymers 213
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7.2.4 Aging and other Relaxations 214
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7.2.5 Piezoelectric Polymers 214
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7.2.6 Asphalt 214
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7.3 Metals 215
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7.3.1 Linear Regime of Metals 215
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7.3.2 Nonlinear Regime of Metals 217
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7.3.3 High-Damping Metals and Alloys 219
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7.3.4 Creep-Resistant Alloys 224
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7.3.5 Semiconductors and Amorphous Elements 225
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7.3.6 Semiconductors and Acoustic Amplification 226
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7.3.7 Nanoscale Properties 226
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7.4 Ceramics 227
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7.4.1 Rocks 227
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7.4.2 Concrete 229
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7.4.3 Inorganic Glassy Materials 231
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7.4.4 Ice 231
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7.4.5 Piezoelectric Ceramics 232
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7.5 Biological Composite Materials 233
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7.5.1 Constitutive Equations 234
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7.5.2 Hard Tissue: Bone 234
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7.5.3 Collagen, Elastin, Proteoglycans 236
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7.5.4 Ligament and Tendon 237
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7.5.5 Muscle 240
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7.5.6 Fat 243
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7.5.7 Brain 243
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7.5.8 Vocal Folds 244
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7.5.9 Cartilage and Joints 244
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7.5.10 Kidney and Liver 246
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7.5.11 Uterus and Cervix 246
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7.5.12 Arteries 247
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7.5.13 Lung 248
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7.5.14 The Ear 248
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7.5.15 The Eye 249
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7.5.16 Tissue Comparison 251
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7.5.17 Plant Seeds 252
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7.5.18 Wood 252
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7.5.19 Soft Plant Tissue: Apple, Potato 253
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7.6 Common Aspects 253
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7.6.1 Temperature Dependence 253
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7.6.2 High-Temperature Background 254
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7.6.3 Negative Damping and Acoustic Emission 255
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7.7 Summary 255
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7.8 Examples 255
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7.9 Problems 256
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Bibliography 257
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8 Causal Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
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8.1 Introduction 271
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8.1.1 Rationale 271
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8.1.2 Survey of Viscoelastic Mechanisms 271
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8.1.3 Coupled Fields 273
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8.2 Thermoelastic Relaxation 274
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8.2.1 Thermoelasticity in One Dimension 274
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8.2.2 Thermoelasticity in Three Dimensions 275
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8.2.3 Thermoelastic Relaxation Kinetics 276
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8.2.4 Heterogeneity and Thermoelastic Damping 278
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8.2.5 Material Properties and Thermoelastic Damping 280
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8.3 Relaxation by Stress-Induced Fluid Motion 280
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8.3.1 Fluid Motion in One Dimension 280
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8.3.2 Biot Theory: Fluid Motion in Three Dimensions 281
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8.4 Relaxation by Molecular Rearrangement 286
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8.4.1 Glassy Region 286
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8.4.2 Transition Region 287
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8.4.3 Rubbery Behavior 289
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8.4.4 Crystalline Polymers 291
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8.4.5 Biological Macromolecules 292
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8.4.6 Polymers and Metals 292
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8.5 Relaxation by Interface Motion 292
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8.5.1 Grain Boundary Slip in Metals 292
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8.5.2 Interface Motion in Composites 294
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8.5.3 Structural Interface Motion 294
4 P( p8 u- c" ]
8.6 Relaxation Processes in Crystalline Materials 294
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8.6.1 Snoek Relaxation: Interstitial Atoms 294
, E1 j6 Z) |& d
8.6.2 Zener Relaxation in Alloys: Pairs of Atoms 298
9 B, h, @7 z# s" }$ ^
8.6.3 Gorsky Relaxation 299
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8.6.4 Granato–L ¨ ucke Relaxation: Dislocations 300
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8.6.5 Bordoni Relaxation: Dislocation Kinks 303
, M2 j4 Z* ^, T0 k
8.6.6 Relaxation Due to Phase Transformations 305
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8.6.7 High-Temperature Background 314
8 g5 h3 B) ~! v# B; a' a$ D+ B1 h
8.6.8 Nonremovable Relaxations 315
0 r5 H, \+ D# X, v
8.6.9 Damping Due to Wave Scattering 316
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8.7 Magnetic and Piezoelectric Materials 316
/ j9 R# l) j. r7 j" @/ Z1 \
8.7.1 Relaxation in Magnetic Media 316
9 \1 x/ F n9 ]- x
8.7.2 Relaxation in Piezoelectric Materials 318
$ |: S* x" z4 x1 ~
8.8 Nonexponential Relaxation 322
% |1 j! i4 h" k% i3 q( T
8.9 Concepts for Material Design 323
1 v2 m" ^, B' m! e3 i- C
8.9.1 Multiple Causes: Deformation Mechanism Maps 323
, |9 ~* a7 ~ d6 ~. {, P
8.9.2 Damping Mechanisms in High-Loss Alloys 326
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8.9.3 Creep Mechanisms in Creep-Resistant Alloys 326
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8.10 Relaxation at Very Long Times 327
1 S, N" k0 Y" r
8.11 Summary 327
9 F3 V0 Y- L, B: ~, z! l4 p9 E" Z$ [
8.12 Examples 328
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8.13 Problems and Questions 332
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Bibliography 332
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9 Viscoelastic Composite Materials . . . . . . . . . . . . . . . . . . . . . . . 341
2 q# k. S( f* Y" M: M2 N
9.1 Introduction 341
2 q4 h" T! \& `( [2 f
9.2 Composite Structures and Properties 341
# X {& [2 O! Q' G0 }/ y6 E6 g, e
9.2.1 Ideal Structures 341
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9.2.2 Anisotropy due to Structure 342
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9.3 Prediction of Elastic and Viscoelastic Properties 344
3 @( r# k. F9 Y' i6 k
9.3.1 Basic Structures: Correspondence Solutions 344
+ D9 W8 z' I; j# b
9.3.2 Voigt Composite 345
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9.3.3 Reuss Composite 345
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9.3.4 Hashin–Shtrikman Composite 346
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9.3.5 Spherical Particulate Inclusions 347
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9.3.6 Fiber Inclusions 349
; W7 S" h0 d+ ^
9.3.7 Platelet Inclusions 349
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9.3.8 Stiffness-Loss Maps 350
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9.4 Bounds on the Viscoelastic Properties 353
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9.5 Extremal Composites 354
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9.6 Biological Composite Materials 356
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9.7 Poisson’s Ratio of Viscoelastic Composites 357
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9.8 Particulate and Fibrous Composite Materials 358
~6 T. l0 u) G2 i4 o2 e
9.8.1 Structure 358
7 d9 v+ i7 }' U
9.8.2 Particulate Polymer Matrix Composites 359
6 ?0 S+ j3 s2 H
9.8.3 Fibrous Polymer Matrix Composites 361
5 T6 ]* S1 v1 V
9.8.4 Metal–Matrix Composites 362
6 [" S( V3 p7 n" z8 k0 F
9.9 Cellular Solids 363
# G# x E' j. w% r y
9.10 Piezoelectric Composites 366
5 \7 u; `# ?, O3 G0 q
9.11 Dispersion of Waves in Composites 366
. V' U3 a9 n9 C2 J& t5 d
9.12 Summary 367
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9.13 Examples 367
9 p" P7 _7 {3 k, p Z, q. Y
9.14 Problems 370
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Bibliography 370
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10 Applications and Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . 377
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10.1 Introduction 377
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10.2 A Viscoelastic Earplug: Use of Recovery 377
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10.3 Creep and Relaxation of Materials and Structures 378
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10.3.1 Concrete 378
6 j& q% ?5 S& t% u
10.3.2 Wood 378
7 W( T% L' a/ _9 D! K
10.3.3 Power Lines 379
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10.3.4 Glass Sag: Flowing Window Panes 380
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10.3.5 Indentation: Road Rutting 380
+ H' N% o8 `& \
10.3.6 Leather 381
5 @+ Q8 j% X& e, j0 c) ?
10.3.7 Creep-Resistant Alloys and Turbine Blades 381
3 L6 F! \6 H7 W4 A
10.3.8 Loosening of Bolts and Screws 382
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10.3.9 Computer Disk Drive: Case Study of Relaxation 384
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10.3.10 Earth, Rock, and Ice 385
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10.3.11 Solder 386
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10.3.12 Filamentsi nL ight Bulbs and Other Devices 387
! E) d( D+ B1 o
10.3.13Tires: Flat-Spotting and Swelling 388
. }+ l+ B. F3 `! `! w4 k8 a
10.3.14Cushionsfor Seats and Wheelchairs 388
! {# L! _2 }+ g8 ] M; v+ F4 M
10.3.15 Artificial Joints 389
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10.3.16 Dental Fillings 389
7 i- T1 T* C: m- U
10.3.17 Food Products 389
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10.3.18 Seals and Gaskets 390
9 G& c0 _( J1 U
10.3.19 Relaxationi nM usical Instrument Strings 390
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10.3.20 Winding of Tape 391
# I O4 e" J/ G
10.4 Creep and Recovery in Human Tissue 391
7 R S" v1 Z" g: u
10.4.1 Spinal Discs: Height Change 391
' |5 N( [4 l V2 v
10.4.2 The Nose 392
; n- o9 x; ?2 e* P) S9 s
10.4.3 Skin 392
+ O. O9 v* X; D8 k
10.4.4 The Head 393
3 g# ]! P4 m. I" S, f* A: t3 V
10.5 Creep Damage and Creep Rupture 394
3 E* M5 v, Q5 l" s
10.5.1 Vajont Slide 394
' F- G) ~# p" W: e
10.5.2 Collapse of a Tunnel Segment 394
{$ I; @) d* ?9 U, K
10.6 Vibration Control and Waves 394
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10.6.1 Analysis of Vibration Transmission 394
" {3 F' q3 z' O( Q' `
10.6.2 Resonant (Tuned) Damping 397
9 I- i6 h8 [, D5 B" T
10.6.3 Rotating Equipment Vibration 397
- s* a2 B4 L2 @& K/ X
10.6.4 Large Structure Vibration: Bridges and Buildings 398
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10.6.5 Damping Layers for Plate and Beam Vibration 399
2 b1 j$ I3 J; u1 o6 ?" z
10.6.6 Structural Damping Materials 400
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10.6.7 Piezoelectric Transducers 402
4 l5 s- R$ \" G% a Q8 D
10.6.8 Aircraft Noise and Vibration 402
, a b& n) i" v- _
10.6.9 Solid Fuel Rocket Vibration 404
. R7 X7 F( l" J% I) q2 I! g$ Q
10.6.10 Sports Equipment Vibration 404
) Q# a* r# n: {5 {1 @6 W
10.6.11 Seat Cushions and Automobiles: Protection of People 404
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10.6.12 Vibrationi n ScientificI nstruments 406
: }9 u. Z% A2 S' j$ Y6 ?1 J
10.6.13 Waves 406
5 n8 U/ f" k& O% V
10.7 “Smart” Materials and Structures 407
% \' H9 u* ?0 i- `8 A& A( `* m! j
10.7.1 “Smart” Materials 407
; `9 R7 o& q3 I5 S
10.7.2 Shape Memory Materials 408
& \8 c- B2 a& F0 H
10.7.3 Self-Healing Materials 409
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10.7.4 Piezoelectric Solid Damping 409
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10.7.5 Active Vibration Control: “Smart” Structures 409
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10.8 Rolling Friction 409
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10.8.1 Rolling Analysis 410
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10.8.2 Rolling of Tires 411
d4 C, e( c1 P U* R) p
10.9 Uses of Low-Loss Materials 412
# A$ \0 ]9 C+ r0 H- N- {1 d/ V
10.9.1 Timepieces 412
5 o( k0 H3 v1 O. c q' l% K
10.9.2 Frequency Stabilization and Control 413
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10.9.3 Gravitational Measurements 413
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10.9.4 Nanoscale Resonators 414
3 E+ e! A/ l8 L; L# S9 c; g
10.10 Impulses, Rebound, and Impact Absorption 414
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10.10.1 Rationale 414
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10.10.2 Analysis 415
$ u+ p3 T( {- P+ k1 n2 V( Y. L
10.10.3 Bumpers and Pads 418
' D' k- e3 A2 R' _* u' T) l, g
10.10.4 Shoe Insoles, Athletic Tracks, and Glove Liners 419
* `1 g! E8 p! S- y8 [6 T
10.10.5 Toughness of Materials 419
8 P- Y$ ~2 V, H
10.10.6 Tissue Viscoelasticity in Medical Diagnosis 420
* `" g4 {! ]8 m4 D
10.11Rebound of a Ball 421
6 H/ C5 _' G; F
10.11.1 Analysis 421
7 x6 N7 c, E3 j7 s6 F& u7 t, b
10.11.2 Applications in Sports 422
! V, B8 a: p& t8 i5 o p: [
10.12 Applications of Soft Materials 424
" C% V; J6 |, q4 R
10.12.1 Viscoelastic Gels in Surgery 424
7 n; P! {9 O& } W, Z) D- m. `) D2 K
10.12.2 Hand Strength Exerciser 424
B! \ ] _' V% w+ o* D* W
10.12.3 Viscoelastic Toys 424
$ ~9 M) w3 V* O z5 W; R' B% h
10.12.4 No-Slip Flooring, Mats, and Shoe Soles 425
; V6 B/ j, L2 W- J3 c: O% ~
10.13 Applications Involving Thermoviscoelasticity 425
" n, v2 d' v. t2 R/ p# e: F; I1 ^( N3 j3 V
10.14 Satellite Dynamics and Stability 426
. B: W5 t- D2 u9 y" i
10.15 Summary 428
1 G8 f- n& `3 S; C' B5 n6 U! c
10.16 Examples 429
& X# \" [% V8 F! Q& H' Y! d z3 {
10.17 Problems 431
" B' N! x9 u2 c3 T& H: r
Bibliography 431
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A: Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
% d( N& p9 q3 K7 n0 a& S! G
A.1 Mathematical Preliminaries 441
6 o# @. W- e+ Y: D. Q4 Z' X
A.1.1 Introduction 441
4 W r6 t. B% v! w- g: h
A.1.2 Functionals and Distributions 441
- U+ o8 i( C9 O2 Z* p, ?
A.1.3 Heaviside Unit Step Function 442
1 O3 o) H; u, T6 k1 c5 b. B
A.1.4 Dirac Delta 442
* h- t7 S, V+ b4 g$ q- ^
A.1.5 Doublet 443
+ X! b2 m% }0 M3 a- i8 H2 W
A.1.6 Gamma Function 445
# D G4 S. _( t t3 p! I
A.1.7 Liebnitz Rule 445
; t* A$ p- P8 p% }+ G. J6 N: `+ l
A.2 Transforms 445
' q# x0 b) q5 D: d/ w' H
A.2.1 Laplace Transform 446
9 W m0 B" t, Z( W" Z
A.2.2 Fourier Transform 446
& H3 b( Y8 k+ i( T. Q/ Z9 k7 r
A.2.3 Hartley Transform 447
1 I: j R7 ~! M. Z
A.2.4 Hilbert Transform 447
. j* W7 {& A/ O: F- v" u. v5 c4 x
A.3 Laplace Transform Properties 448
A* e8 l; o$ R4 M5 V* W6 v
A.4 Convolutions 449
9 Y5 [* }1 Y+ w% Y: e% O6 _6 P
A.5 Interrelations in Elasticity Theory 451
3 T- G6 x! O$ u6 F9 `
A.6 Other Works on Viscoelasticity 451
8 x; W$ x& i1 T+ t8 ^
Bibliography 452
9 {0 U8 x& `3 P7 m6 @
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B: Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
2 f8 p4 u k$ C0 Y- w7 E
B.1 Principal Symbols 455
) W; D8 N5 w5 W0 |$ {" Y
Index 457
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9 t) s$ e" ^# M( ^' K! C
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