Active and passive vibration damping. (2018)

• Record Type: Book
• Further Information: Note: Amr M. Baz.
• Authors: Baz, Amr Mahmoud Sabry, 1945-
• Contents: Preface xvii List of Symbols xxi Abbreviations xxxi Part I Fundamentals of Viscoelastic Damping 1 1 Vibration Damping 3 1.1 Overview 3 1.2 Passive, Active, and Hybrid Vibration Control 3 1.2.1 Passive Damping 3 1.2.1.1 Free and Constrained Damping Layers 3 1.2.1.2 Shunted Piezoelectric Treatments 4 1.2.1.3 Damping Layers with Shunted Piezoelectric Treatments 5 1.2.1.4 Magnetic Constrained Layer Damping (MCLD) 5 1.2.1.5 Damping with Shape Memory Fibers 6 1.2.2 Active Damping 6 1.2.3 Hybrid Damping 7 1.2.3.1 Active Constrained Layer Damping (ACLD) 7 1.2.3.2 Active Piezoelectric Damping Composites (APDC) 7 1.2.3.3 Electromagnetic Damping Composites (EMDC) 8 1.2.3.4 Active Shunted Piezoelectric Networks 8 1.3 Summary 9 References 9 2 Viscoelastic Damping 11 2.1 Introduction 11 2.2 Classical Models of Viscoelastic Materials 11 2.2.1 Characteristics in the Time Domain 11 2.2.2 Basics for Time Domain Analysis 12 2.2.3 Detailed Time Response of Maxwell and Kelvin–Voigt Models 14 2.2.4 Detailed Time Response of the Poynting–Thomson Model 17 2.3 Creep Compliance and Relaxation Modulus 20 2.3.1 Direct Laplace Transformation Approach 22 2.3.2 Approach of Simultaneous Solution of a Linear Set of Equilibrium, Kinematic, and Constitutive Equations 23 2.4 Characteristics of the VEM in the Frequency Domain 25 2.5 Hysteresis and Energy Dissipation Characteristics of Viscoelastic Materials 27 2.5.1 Hysteresis Characteristics 27 2.5.2 Energy Dissipation 28 2.5.3 Loss Factor 28 2.5.3.1 Relationship between Dissipation and Stored Elastic Energies 28 2.5.3.2 Relationship between Different Strains 29 2.5.4 Storage Modulus 29 2.6 Fractional Derivative Models of Viscoelastic Materials 32 2.6.1 Basic Building Block of Fractional Derivative Models 32 2.6.2 Basic Fractional Derivative Models 33 2.6.3 Other Common Fractional Derivative Models 36 2.7 Viscoelastic versus Other Types of Damping Mechanisms 38 2.8 Summary 40 References 40 3 Characterization of the Properties of Viscoelastic Materials 57 3.1 Introduction 57 3.2 Typical Behavior of Viscoelastic Materials 57 3.3 Frequency Domain Measurement Techniques of the Dynamic Properties of Viscoelastic Material 59 3.3.1 Dynamic, Mechanical, and Thermal Analyzer 60 3.3.2 Oberst Test Beam Method 64 3.3.2.1 Set-Up and Beam Configurations 64 3.3.2.2 Parameter Extraction 66 3.4 Master Curves of Viscoelastic Materials 68 3.4.1 The Principle of Temperature-Frequency Superposition 68 3.4.2 The Use of the Master Curves 71 3.4.3 The Constant Temperature Lines 71 3.5 Time-Domain Measurement Techniques of the Dynamic Properties of Viscoelastic Materials 72 3.5.1 Creep and Relaxation Measurement Methods 73 3.5.1.1 Testing Equipment 73 3.5.1.2 Typical Creep and Relaxation Behavior 74 3.5.1.3 Time-Temperature Superposition 76 3.5.1.4 Boltzmann Superposition Principle 78 3.5.1.5 Relationship between the Relaxation Modulus and Complex Modulus 80 3.5.1.6 Relationship between the Creep Compliance and Complex Compliance 81 3.5.1.7 Relationship between the Creep Compliance and Relaxation Modulus 83 3.5.1.8 Alternative Relationship between the Creep Compliance and Complex Compliance 83 3.5.1.9 Alternative Relationship between the Relaxation Modulus and Complex Modulus 84 3.5.1.10 Summary of the Basic Interconversion Relationship 85 3.5.1.11 Practical Issues in Implementation of Interconversion Relationships 86 3.5.2 Split Hopkinson Pressure Bar Method 94 3.5.2.1 Overview 94 3.5.2.2 Theory of 1D SHPB 95 3.5.2.3 Complex Modulus of a VEM from SHPB Measurements 98 3.5.3 Wave Propagation Method 105 3.5.4 Ultrasonic Wave Propagation Method 109 3.5.4.1 Overview 109 3.5.4.2 Theory 109 3.5.4.3 Measurement of the Phase Velocity and Attenuation Factor 111 3.5.4.4 Typical Attenuation Factors 113 3.6 Summary 115 References 116 4 Viscoelastic Materials 127 4.1 Introduction 127 4.2 Golla–Hughes–McTavish (GHM) Model 127 4.2.1 Motivation of the GHM Model 128 4.2.2 Computation of the Parameters of the GHM Mini-Oscillators 132 4.2.3 On the Structure of the GHM Model 135 4.2.3.1 Other Forms of GHM Structures 135 4.2.3.2 Relaxation Modulus of the GHM Model 135 4.2.4 Structural Finite Element Models of Rods Treated with VEM 137 4.2.4.1 Unconstrained Layer Damping 138 4.2.4.2 Constrained Layer Damping 142 4.3 Structural Finite Element Models of Beams Treated with VEM 150 4.3.1 Degrees of Freedom 150 4.3.2 Basic Kinematic Relationships 151 4.3.3 Stiffness and Mass Matrices of the Beam/VEM Element 152 4.3.4 Equations of Motion of the Beam/VEM Element 153 4.4 Generalized Maxwell Model (GMM) 155 4.4.1 Overview 155 4.4.2 Internal Variable Representation of the GMM 157 4.4.2.1 Single-DOF System 157 4.4.2.2 Multi-Degree of Freedom System 158 4.4.2.3 Condensation of the Internal Degrees of Freedom 159 4.4.2.4 Direct Solution of Coupled Structural and Internal Degrees of Freedom 160 4.5 Augmenting Thermodynamic Field (ATF) Model 163 4.5.1 Overview 163 4.5.2 Equivalent Damping Ratio of the ATF Model 164 4.5.3 Multi-degree of Freedom ATF Model 165 4.5.4 Integration with a Finite Element Model 165 4.6 Fractional Derivative (FD) Models 167 4.6.1 Overview 167 4.6.2 Internal Degrees of Freedom of Fractional Derivative Models 169 4.6.3 Grunwald Approximation of Fractional Derivative 169 4.6.4 Integration Fractional Derivative Approximation with Finite Element 170 4.6.4.1 Viscoelastic Rod 170 4.6.4.2 Beam with Passive Constrained Layer Damping (PCLD) Treatment 172 4.7 Finite Element Modeling of Plates Treated with Passive Constrained Layer Damping 176 4.7.1 Overview 176 4.7.2 The Stress and Strain Characteristics 178 4.7.2.1 The Plate and the Constraining Layers 178 4.7.2.2 The VEM Layer 179 4.7.3 The Potential and Kinetic Energies 179 4.7.4 The Shape Functions 179 4.7.5 The Stiffness Matrices 181 4.7.6 The Mass Matrices 181 4.7.7 The Element and Overall Equations of Motion 182 4.8 Finite Element Modeling of Shells Treated with Passive Constrained Layer Damping 185 4.8.1 Overview 185 4.8.2 Stress–Strain Relationships 186 4.8.2.1 Shell and Constraining Layer 186 4.8.2.2 Viscoelastic Layer 187 4.8.3 Kinetic and Potential Energies 189 4.8.4 The Shape Functions 189 4.8.5 The Stiffness Matrices 189 4.8.6 The Mass Matrices 190 4.8.7 The Element and Overall Equations of Motion 191 4.9 Summary 192 References 196 5 Finite Element Modeling of Viscoelastic Damping by Modal Strain Energy Method 205 5.1 Introduction 205 5.2 Modal Strain Energy (MSE) Method 205 5.3 Modified Modal Strain Energy (MSE) Methods 210 5.3.1 Weighted Stiffness Matrix Method (WSM) 210 5.3.2 Weighted Storage Modulus Method (WSTM) 211 5.3.3 Improved Reduction System Method (IRS) 211 5.3.4 Low Frequency Approximation Method (LFA) 213 5.4 Summary of Modal Strain Energy Methods 215 5.5 Modal Strain Energy as a Metric for Design of Damping Treatments 215 5.6 Perforated Damping Treatments 220 5.6.1 Overview 220 5.6.2 Finite Element Modeling 222 5.6.2.1 Element Energies 224 5.6.2.2 Topology Optimiz
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 620.37; Damping (Mechanics); Vibration
• Languages: English
• ISBNs: 9781118537602
• Related ISBNs: 9781118537589; 9781118537572
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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