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Part II: Advanced Damping Treatments
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Part II: Advanced Damping Treatments
by Amr M. Baz
Active and Passive Vibration Damping
Cover
Preface
List of Symbols
Abbreviations
Part I: Fundamentals of Viscoelastic Damping
1 Vibration Damping
1.1 Overview
1.2 Passive, Active, and Hybrid Vibration Control
1.3 Summary
References
2 Viscoelastic Damping
2.1 Introduction
2.2 Classical Models of Viscoelastic Materials
2.3 Creep Compliance and Relaxation Modulus
2.4 Characteristics of the VEM in the Frequency Domain
2.5 Hysteresis and Energy Dissipation Characteristics of Viscoelastic Materials
2.6 Fractional Derivative Models of Viscoelastic Materials
2.7 Viscoelastic Versus Other Types of Damping Mechanisms
2.8 Summary
References
2.A Initial and Final Value Theorems
2.B Fractional Calculus
Problems
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
3.4 Master Curves of Viscoelastic Materials
3.5 Time‐Domain Measurement Techniques of the Dynamic Properties of Viscoelastic Materials
3.6 Summary
References
3.A Convolution Theorem
Problems
4 Viscoelastic Materials
4.1 Introduction
4.2 Golla–Hughes–McTavish (GHM) Model
4.3 Structural Finite Element Models of Beams Treated with VEM
4.4 Generalized Maxwell Model (GMM)
4.5 Augmenting Thermodynamic Field (ATF) Model
4.6 Fractional Derivative (FD) Models
4.7 Finite Element Modeling of Plates Treated with Passive Constrained Layer Damping
4.8 Finite Element Modeling of Shells Treated with Passive Constrained Layer Damping
4.9 Summary
References
Problems
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
5.4 Summary of Modal Strain Energy Methods
5.5 Modal Strain Energy as a Metric for Design of Damping Treatments
5.6 Perforated Damping Treatments
5.7 Summary
References
Problems
6 Energy Dissipation in Damping Treatments
6.1 Introduction
6.2 Passive Damping Treatments of Rods
6.3 Active Constrained Layer Damping Treatments of Rods
6.4 Passive Constrained Layer Damping Treatments of Beams
6.5 Active Constrained Layer Damping Treatments of Beams
6.6 Passive and Active Constrained Layer Damping Treatments of Plates
6.7 Passive and Active Constrained Layer Damping Treatments of Axi‐Symmetric Shells
6.8 Summary
References
6.A Basic Identities
6.B Piezoelectricity*
Problems
Part II: Advanced Damping Treatments
7 Vibration Damping of Structures Using Active Constrained Layer Damping
7.1 Introduction
7.2 Motivation for Using Passive and Active Constrained Layer Damping
7.3 Active Constrained Layer Damping for Beams
7.4 Active Constrained Layer Damping for Plates
7.5 Active Constrained Layer Damping for Shells
7.6 Summary
References
7.A Piezoelectric Sensor Basic Equations
Problems
8 Advanced Damping Treatments
8.1 Introduction
8.2 Stand‐Off Damping Treatments
8.3 Functionally Graded Damping Treatments
8.4 Passive and Active Damping Composite Treatments
8.5 Magnetic Damping Treatments
8.6 Negative Stiffness Composites
8.7 Summary
References
8.A Matrices of the Models of a Passive Stand‐Off Layer
8.B The Electromechanical Coupling Factor of One Piezoelectric Rod
8.C Constitutive Equations of APDC
8.D Magnetic Forces in the Passive Magnetic Composite
8.E Stiffness and Mass Matrices Passive Magnetic Composite (PMC)
Problems
9 Vibration Damping with Shunted Piezoelectric Networks
9.1 Introduction
9.2 Shunted Piezoelectric Patches
9.3 Finite Element Modeling of Structures Treated with Shunted Piezo‐Networks
9.4 Active Shunted Piezoelectric Networks
9.5 Multi‐Mode Vibration Control with Shunted Piezoelectric Networks
9.6 Summary
References
9.A Electromechanical Coupling Factor
10 Vibration Control with Periodic Structures
10.1 Introduction
10.2 Basics of Periodic Structures
10.3 Filtering Characteristics of Passive Periodic Structures
10.4 Natural Frequencies, Mode Shapes, and Response of Periodic Structures
10.5 Active Periodic Structures
10.6 Localization Characteristics of Passive and Active Aperiodic Structures
10.7 Periodic Rod with Periodic Shunted Piezoelectric Patches
10.8 Two‐Dimensional Active Periodic Structure
10.9 Periodic Structures with Internal Resonances
10.10 Summary
References
10.A The Wavelet Transform
11 Nanoparticle Damping Composites
11.1 Introduction
11.2 Nanoparticle‐Filled Polymer Composites
11.3 Comparisons with Classical Filler Reinforcement Methods
11.4 Applications of Carbon Black/Polymer Composites
11.5 CB/Polymer Composite as a Shunting Resistance of Piezoelectric Layers
11.6 Hybrid Composites with Shunted Piezoelectric Particles
11.7 Summary
References
11.A Transformation Matrix
11.B Reinforcement Mechanics of Particle‐Filled Polymers
12 Power Flow in Damped Structures
12.1 Introduction
12.2 Vibrational Power
12.3 Vibrational Power Flow in Beams
12.4 Vibrational Power of Plates
12.5 Power Flow and Structural Intensity for Shells
12.6 Summary
References
12.A Calculation of Power Flow in ANSYS
Glossary
Appendix A: Complex Modulus of Typical Damping Treatments
A.1 3M Viscoelastic Damping Polymers
A.2 E.A.R. Viscoelastic Damping Polymers
A.3 Soundcoat Viscoelastic Damping Polymers
Major Viscoelastic Material Manufacturers Websites
Further Reading
Index
End User License Agreement
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6 Energy Dissipation in Damping Treatments
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7 Vibration Damping of Structures Using Active Constrained Layer Damping
Part II
Advanced Damping Treatments
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