Active and Passive Vibration Damping.
- 1st ed.
- 1 online resource (754 pages)
Intro -- Title Page -- Copyright Page -- Contents -- Preface -- List of Symbols -- Abbreviations -- Part I Fundamentals of Viscoelastic Damping -- Chapter 1 Vibration Damping -- 1.1 Overview -- 1.2 Passive, Active, and Hybrid Vibration Control -- 1.2.1 Passive Damping -- 1.2.1.1 Free and Constrained Damping Layers -- 1.2.1.2 Shunted Piezoelectric Treatments -- 1.2.1.3 Damping Layers with Shunted Piezoelectric Treatments -- 1.2.1.4 Magnetic Constrained Layer Damping (MCLD) -- 1.2.1.5 Damping with Shape Memory Fibers -- 1.2.2 Active Damping -- 1.2.3 Hybrid Damping -- 1.2.3.1 Active Constrained Layer Damping (ACLD) -- 1.2.3.2 Active Piezoelectric Damping Composites (APDC) -- 1.2.3.3 Electromagnetic Damping Composites (EMDC) -- 1.2.3.4 Active Shunted Piezoelectric Networks -- 1.3 Summary -- References -- Chapter 2 Viscoelastic Damping -- 2.1 Introduction -- 2.2 Classical Models of Viscoelastic Materials -- 2.2.1 Characteristics in the Time Domain -- 2.2.2 Basics for Time Domain Analysis -- 2.2.3 Detailed Time Response of Maxwell and Kelvin-Voigt Models -- 2.2.4 Detailed Time Response of the Poynting-Thomson Model -- 2.3 Creep Compliance and Relaxation Modulus -- 2.3.1 Direct Laplace Transformation Approach -- 2.3.2 Approach of Simultaneous Solution of a Linear Set of Equilibrium, Kinematic, and Constitutive Equations -- 2.4 Characteristics of the VEM in the Frequency Domain -- 2.5 Hysteresis and Energy Dissipation Characteristics of Viscoelastic Materials -- 2.5.1 Hysteresis Characteristics -- 2.5.2 Energy Dissipation -- 2.5.3 Loss Factor -- 2.5.3.1 Relationship Between Dissipation and Stored Elastic Energies -- 2.5.3.2 Relationship Between Different Strains -- 2.5.4 Storage Modulus -- 2.6 Fractional Derivative Models of Viscoelastic Materials -- 2.6.1 Basic Building Block of Fractional Derivative Models -- 2.6.2 Basic Fractional Derivative Models. 2.6.3 Other Common Fractional Derivative Models -- 2.7 Viscoelastic Versus Other Types of Damping Mechanisms -- 2.8 Summary -- References -- 2.A Initial and Final Value Theorems -- 2.B Fractional Calculus -- 2.B.1 Fractional Integration -- 2.B.2 Convolution Theorem -- 2.B.3 Fractional Derivatives -- 2.B.4 Laplace Transform of Fractional Derivatives -- 2.B.5 Grunwald-Letnikov Definition of Fractional Derivatives -- Problems -- Chapter 3 Characterization of the Properties of Viscoelastic Materials -- 3.1 Introduction -- 3.2 Typical Behavior of Viscoelastic Materials -- 3.3 Frequency Domain Measurement Techniques of the Dynamic Properties of Viscoelastic Material -- 3.3.1 Dynamic, Mechanical, and Thermal Analyzer -- 3.3.2 Oberst Test Beam Method -- 3.3.2.1 Set-Up and Beam Configurations -- 3.3.2.2 Parameter Extraction -- 3.4 Master Curves of Viscoelastic Materials -- 3.4.1 The Principle of Temperature-Frequency Superposition -- 3.4.2 The Use of the Master Curves -- 3.4.3 The Constant Temperature Lines -- 3.5 Time-Domain Measurement Techniques of the Dynamic Properties of Viscoelastic Materials -- 3.5.1 Creep and Relaxation Measurement Methods -- 3.5.1.1 Testing Equipment -- 3.5.1.2 Typical Creep and Relaxation Behavior -- 3.5.1.3 Time-Temperature Superposition -- 3.5.1.4 Boltzmann Superposition Principle -- 3.5.1.5 Relationship Between the Relaxation Modulus and Complex Modulus -- 3.5.1.6 Relationship Between the Creep Compliance and Complex Compliance -- 3.5.1.7 Relationship Between the Creep Compliance and Relaxation Modulus -- 3.5.1.8 Alternative Relationship Between the Creep Compliance and Complex Compliance -- 3.5.1.9 Alternative Relationship Between the Relaxation Modulus and Complex Modulus -- 3.5.1.10 Summary of the Basic Interconversion Relationship -- 3.5.1.11 Practical Issues in Implementation of Interconversion Relationships. 3.5.2 Split Hopkinson Pressure Bar Method -- 3.5.2.1 Overview -- 3.5.2.2 Theory of 1D SHPB -- 3.5.2.3 Complex Modulus of a VEM from SHPB Measurements -- 3.5.3 Wave Propagation Method -- 3.5.4 Ultrasonic Wave Propagation Method -- 3.5.4.1 Overview -- 3.5.4.2 Theory -- 3.5.4.3 Measurement of the Phase Velocity and Attenuation Factor -- 3.5.4.4 Typical Attenuation Factors -- 3.6 Summary -- References -- 3.A Convolution Theorem -- Problems -- Chapter 4 Viscoelastic Materials -- 4.1 Introduction -- 4.2 Golla-Hughes-McTavish (GHM) Model -- 4.2.1 Motivation of the GHM Model -- 4.2.2 Computation of the Parameters of the GHM Mini-Oscillators -- 4.2.3 On the Structure of the GHM Model -- 4.2.3.1 Other Forms of GHM Structures -- 4.2.3.2 Relaxation Modulus of the GHM Model -- 4.2.4 Structural Finite Element Models of Rods Treated with VEM -- 4.2.4.1 Unconstrained Layer Damping -- 4.2.4.2 Constrained Layer Damping -- 4.3 Structural Finite Element Models of Beams Treated with VEM -- 4.3.1 Degrees of Freedom -- 4.3.2 Basic Kinematic Relationships -- 4.3.3 Stiffness and Mass Matrices of the Beam/VEM Element -- 4.3.4 Equations of Motion of the Beam/VEM Element -- 4.4 Generalized Maxwell Model (GMM) -- 4.4.1 Overview -- 4.4.2 Internal Variable Representation of the GMM -- 4.4.2.1 Single-DOF System -- 4.4.2.2 Multi-Degree of Freedom System -- 4.4.2.3 Condensation of the Internal Degrees of Freedom -- 4.4.2.4 Direct Solution of Coupled Structural and Internal Degrees of Freedom -- 4.5 Augmenting Thermodynamic Field (ATF) Model -- 4.5.1 Overview -- 4.5.2 Equivalent Damping Ratio of the ATF Model -- 4.5.3 Multi-degree of Freedom ATF Model -- 4.5.4 Integration with a Finite Element Model -- 4.6 Fractional Derivative (FD) Models -- 4.6.1 Overview -- 4.6.2 Internal Degrees of Freedom of Fractional Derivative Models -- 4.6.3 Grunwald Approximation of Fractional Derivative. 4.6.4 Integration Fractional Derivative Approximation with Finite Element -- 4.6.4.1 Viscoelastic Rod -- 4.6.4.2 Beam with Passive Constrained Layer Damping (PCLD) Treatment -- 4.7 Finite Element Modeling of Plates Treated with Passive Constrained Layer Damping -- 4.7.1 Overview -- 4.7.2 The Stress and Strain Characteristics -- 4.7.2.1 The Plate and the Constraining Layers -- 4.7.2.2 The VEM Layer -- 4.7.3 The Potential and Kinetic Energies -- 4.7.4 The Shape Functions -- 4.7.5 The Stiffness Matrices -- 4.7.6 The Mass Matrices -- 4.7.7 The Element and Overall Equations of Motion -- 4.8 Finite Element Modeling of Shells Treated with Passive Constrained Layer Damping -- 4.8.1 Overview -- 4.8.2 Stress-Strain Relationships -- 4.8.2.1 Shell and Constraining Layer -- 4.8.2.2 Viscoelastic Layer -- 4.8.3 Kinetic and Potential Energies -- 4.8.4 The Shape Functions -- 4.8.5 The Stiffness Matrices -- 4.8.6 The Mass Matrices -- 4.8.7 The Element and Overall Equations of Motion -- 4.9 Summary -- References -- Problems -- Chapter 5 Finite Element Modeling of Viscoelastic Damping by Modal Strain Energy Method -- 5.1 Introduction -- 5.2 Modal Strain Energy (MSE) Method -- 5.3 Modified Modal Strain Energy (MSE) Methods -- 5.3.1 Weighted Stiffness Matrix Method (WSM) -- 5.3.2 Weighted Storage Modulus Method (WSTM) -- 5.3.3 Improved Reduction System Method (IRS) -- 5.3.4 Low Frequency Approximation Method (LFA) -- 5.4 Summary of Modal Strain Energy Methods -- 5.5 Modal Strain Energy as a Metric for Design of Damping Treatments -- 5.6 Perforated Damping Treatments -- 5.6.1 Overview -- 5.6.2 Finite Element Modeling -- 5.6.2.1 Element Energies -- 5.6.2.2 Topology Optimization of Unconstrained Layer Damping -- 5.6.2.3 Sensitivity Analysis -- 5.7 Summary -- References -- Problems -- Chapter 6 Energy Dissipation in Damping Treatments -- 6.1 Introduction. 6.2 Passive Damping Treatments of Rods -- 6.2.1 Passive Constrained Layer Damping -- 6.2.1.1 Equation of Motion -- 6.2.1.2 Energy Dissipation -- 6.2.2 Passive Unconstrained Layer Damping -- 6.3 Active Constrained Layer Damping Treatments of Rods -- 6.3.1 Equation of Motion -- 6.3.2 Boundary Control Strategy -- 6.3.3 Energy Dissipation -- 6.4 Passive Constrained Layer Damping Treatments of Beams -- 6.4.1 Basic Equations of Damped Beams -- 6.4.2 Bending Energy of Beams -- 6.4.3 Energy Dissipated in Beams with Passive Constrained Layer Damping -- 6.5 Active Constrained Layer Damping Treatments of Beams -- 6.6 Passive and Active Constrained Layer Damping Treatments of Plates -- 6.6.1 Kinematic Relationships -- 6.6.2 Energies of the PCLD and ACLD Treatments -- 6.6.2.1 The Potential Energies -- 6.6.2.2 The Kinetic Energy -- 6.6.2.3 Work Done -- 6.6.3 The Models of the PCLD and ACLD Treatments -- 6.6.4 Boundary Control of Plates with ACLD Treatments -- 6.6.5 Energy Dissipation and Loss Factors of Plates with PCLD and ACLD Treatments -- 6.7 Passive and Active Constrained Layer Damping Treatments of Axi-Symmetric Shells -- 6.7.1 Background -- 6.7.2 The Concept of the Active Constrained Layer Damping -- 6.7.3 Variational Modeling of the Shell/ACLD System -- 6.7.3.1 Main Assumptions of the Model -- 6.7.3.2 Kinematic Relationships -- 6.7.3.3 Stress-Strain Relationships -- 6.7.3.4 Energies of Shell/ACLD System -- 6.7.3.5 The Model -- 6.7.4 Boundary Control Strategy -- 6.7.4.1 Overview -- 6.7.4.2 Control Strategy -- 6.7.4.3 Implementation of the Boundary Control Strategy -- 6.7.4.4 Transverse Compliance and Longitudinal Deflection -- 6.7.5 Energy Dissipated in the ACLD Treatment of an Axi-Symmetric Shell -- 6.8 Summary -- References -- 6.A Basic Identities -- 6.B Piezoelectricity -- 6.B.1 Piezoelectric Effects -- 6.B.2 Basic Constitutive Equations -- Problems. Part II Advanced Damping Treatments.