Amr M Baz

Active and Passive Vibration Damping

• Gebundenes Buch

Produktbeschreibung

An important work presenting in one volume the application of viscoelastic damping materials to control vibration and noise of structures, machinery, and vehicles Focuses primarily on the application of passive as well as actively treated viscoelastic damping materials to control vibration and noise of structures, machinery, and vehicles. Emphasis is placed on presenting the basic principles and potential applications of passive and active vibration damping technologies. The presentation encompasses a mix between the associated physical fundamentals, governing theories and optimal design strategies of various configurations of vibration damping treatments. Utilization of the smart materials to augment the vibration damping of passive treatments is the common thread which is pursued, in depth, among all the chapters of the book. This book is divided into two parts, the first dealing with materials theory and the second dealing with the practical application to vibrations. It presents the basics of various damping effective treatments such as constrained layers, shunted piezoelectric treatments, electromagnetic and shape memory fibers. Classical aspects of viscoelastic materials models are also analyzed from the experimental characterization of the material coefficients as well as their modeling. New models such as Golla-Hughes-McTavish (GHM ) model, augmented temperature field (ATF) model, fractional derivatives (FD) models. Modal strain energy (MSE) models are also deeply analyzed. Part II of the book is devoted to the detailed descriptions of advanced damping treatments using all the fundamentals presented in Part I. Each chapter of the book ends with a number of problems that cover the different aspects of theoretical analysis, design, and applications of vibration damping technologies. The book has a large number of numerical examples to reinforce the understanding of the theories covered, providing the means for exercising the knowledge gained, and emphasizing the learning of strategies for the design and application of active and passive vibration damping systems. The examples are supported by a set of MATLAB software modules to enable the designers of vibration damping systems to extend the theories presented to various applications. * Written by an internationally recognized authority and pioneer, it summarizes and presents comprehensive coverage in one volume material that until now appears throughout a selection of references * Presents a mix of the associated physical fundamentals, governing theories and optimal design strategies of various configurations of vibration damping treatments, a comprehensive coverage not available elsewhere * With companion website including MATLAB software, solutions to all problems, and power point slides, the supporting tools enable hands-on experience of the analysis, design, optimization, and application to a wide range of situations

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A guide to the application of viscoelastic damping materials to control vibration and noise of structures, machinery, and vehicles Active and Passive Vibration Damping is a practical guide to the application of passive as well as actively treated viscoelastic damping materials to control vibration and noise of structures, machinery and vehicles. The author -- a noted expert on the topic -- presents the basic principles and reviews the potential applications of passive and active vibration damping technologies. The text presents a combination of the associated physical fundamentals, governing theories and the optimal design strategies of various configurations of vibration damping treatments. The text presents the basics of various damping effective treatments such as constrained layers, shunted piezoelectric treatments, electromagnetic and shape memory fibers. Classical and new models are included as well as aspects of viscoelastic materials models that are analyzed from the experimental characterization of the material coefficients as well as their modeling. The use of smart materials to augment the vibration damping of passive treatments is pursued in depth throughout the book. This vital guide: * Contains numerical examples that reinforce the understanding of the theories presented * Offers an authoritative text from an internationally recognized authority and pioneer on the subject * Presents, in one volume, comprehensive coverage of the topic that is not available elsewhere * Presents a mix of the associated physical fundamentals, governing theories and optimal design strategies of various configurations of vibration damping treatments Written for researchers in vibration damping and research, engineers in structural dynamics and practicing engineers, Active and Passive Vibration Damping offers a hands-on resource for applying passive as well as actively treated viscoelastic damping materials to control vibration and noise of structures, machinery and vehicles.

Produktdetails

• Verlag: John Wiley & Sons / Turner Publishing Company
• Seitenzahl: 752
• Erscheinungstermin: 13. Mai 2016
• Englisch
• Abmessung: 251mm x 180mm x 47mm
• Gewicht: 1441g
• ISBN-13: 9781118481929
• ISBN-10: 1118481925
• Artikelnr.: 38106809

Autorenporträt

AMR M. BAZ, PHD, is Minta-Martin Chair Professor and Director of Smart Materials and Structures Research Center, Mechanical Engineering Department, University of Maryland, USA. His research interests include active and passive control of vibration and noise, active constrained layer damping, magnetic composites, virtual reality design of smart structures, active periodic structures, active acoustic meta-materials, and non-reciprocal acoustic metamaterials.

Inhaltsangabe

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 Optimization of Unconstrained Layer Damping
227 5.6.2.3 Sensitivity Analysis 228 5.7 Summary 234 References 234 6
Energy Dissipation in Damping Treatments 243 6.1 Introduction 243 6.2
Passive Damping Treatments of Rods 243 6.2.1 Passive Constrained Layer
Damping 243 6.2.1.1 Equation of Motion 243 6.2.1.2 Energy Dissipation 247
6.2.2 Passive Unconstrained Layer Damping 248 6.3 Active Constrained Layer
Damping Treatments of Rods 251 6.3.1 Equation of Motion 251 6.3.2 Boundary
Control Strategy 253 6.3.3 Energy Dissipation 254 6.4 Passive Constrained
Layer Damping Treatments of Beams 257 6.4.1 Basic Equations of Damped Beams
257 6.4.2 Bending Energy of Beams 258 6.4.3 Energy Dissipated in Beams with
Passive Constrained Layer Damping 258 6.5 Active Constrained Layer Damping
Treatments of Beams 264 6.6 Passive and Active Constrained Layer Damping
Treatments of Plates 267 6.6.1 Kinematic Relationships 268 6.6.2 Energies
of the PCLD and ACLD Treatments 269 6.6.2.1 The Potential Energies 269
6.6.2.2 The Kinetic Energy 269 6.6.2.3 Work Done 269 6.6.3 The Models of
the PCLD and ACLD Treatments 270 6.6.4 Boundary Control of Plates with ACLD
Treatments 270 6.6.5 Energy Dissipation and Loss Factors of Plates with
PCLD and ACLD Treatments 271 6.7 Passive and Active Constrained Layer
Damping Treatments of Axi-Symmetric Shells 274 6.7.1 Background 275 6.7.2
The Concept of the Active Constrained Layer Damping 276 6.7.3 Variational
Modeling of the Shell/ACLD System 276 6.7.3.1 Main Assumptions of the Model
276 6.7.3.2 Kinematic Relationships 276 6.7.3.3 Stress-Strain Relationships
277 6.7.3.4 Energies of Shell/ACLD System 279 6.7.3.5 The Model 280 6.7.4
Boundary Control Strategy 282 6.7.4.1 Overview 282 6.7.4.2 Control Strategy
282 6.7.4.3 Implementation of the Boundary Control Strategy 283 6.7.4.4
Transverse Compliance and Longitudinal Deflection 283 6.7.5 Energy
Dissipated in the ACLD Treatment of an Axi-Symmetric Shell 287 6.8 Summary
288 References 290 Part II Advanced Damping Treatments 301 7 Vibration
Damping of Structures Using Active Constrained Layer Damping 303 7.1
Introduction 303 7.2 Motivation for Using Passive and Active Constrained
Layer Damping 303 7.2.1 Base Structure 304 7.2.2 Structure Treated with
Unconstrained Passive Layer Damping 306 7.2.3 Structure Treated with
Constrained Passive Layer Damping 308 7.2.4 Structure Treated with Active
Constrained Passive Layer Damping 311 7.3 Active Constrained Layer Damping
for Beams 316 7.3.1 Introduction 316 7.3.2 Concept of Active Constrained
Layer Damping 316 7.3.3 Finite Element Modeling of a Beam/ACLD Assembly 318
7.3.3.1 The Model 319 7.3.3.2 Equations of Motion 322 7.3.4
Distributed-Parameter Modeling of a Beam/ACLD Assembly 328 7.3.4.1 Overview
328 7.3.4.2 The Energies and Work Done on the Beam/ACLD Assembly 328
7.3.4.3 The Distributed-Parameter Model 331 7.3.4.4 Globally Stable
Boundary Control Strategy 333 7.3.4.5 Implementation of the Globally Stable
Boundary Control Strategy 333 7.3.4.6 Response of the Beam/ACLD Assembly
334 7.4 Active Constrained Layer Damping for Plates 336 7.4.1 Control
Forces and Moments Generated by the Active Constraining Layer 337 7.4.1.1
The In-Plane Piezoelectric Forces 337 7.4.1.2 The Piezoelectric Moments 338
7.4.1.3 Piezoelectric Sensor 338 7.4.1.4 Control Voltage to Piezoelectric
Constraining Layer 339 7.4.2 Equations of Motion 339 7.5 Active Constrained
Layer Damping for Shells 344 7.5.1 Control Forces and Moments Generated by
the Active Constraining Layer 344 7.5.2 Equations of Motion 344 7.6 Summary
348 References 351 8 Advanced Damping Treatments 361 8.1 Introduction 361
8.2 Stand-Off Damping Treatments 362 8.2.1 Background of Stand-Off Damping
Treatments 362 8.2.2 The Stand-Off Damping Treatments 362 8.2.3
Distributed-Parameter Model of the Stand-Off Layer Damping Treatment 364
8.2.3.1 Kinematic Equations 364 8.2.3.2 Constitutive Equations 365 8.2.4
Distributed Transfer Function Method 369 8.2.5 Finite Element Model 370
8.2.6 Summary 375 8.3 Functionally Graded Damping Treatments 375 8.3.1
Background of Functionally Graded Constrained Layer Damping 375 8.3.2
Concept of Constrained Layer Damping with Functionally Graded Viscoelastic
Cores 376 8.3.3 Finite Element Model 377 8.3.3.1 Quasi-Static Model of the
Passive Constrained Damping Layer of Plunkett and Lee (1970) 377 8.3.3.2
Dispersion Characteristics of Passive Constrained Damping Layer with
Uniform and Functionally Graded Cores 383 8.3.4 Summary 390 8.4 Passive and
Active Damping Composite Treatments 390 8.4.1 Passive Composite Damping
Treatments 390 8.4.2 Active Composite Damping Treatments 394 8.4.3 Finite
Element Modeling of Beam with APDC 396 8.4.3.1 Model and Main Assumptions
396 8.4.3.2 Kinematics 397 8.4.3.3 Degrees of Freedom and Shape Functions
398 8.4.3.4 System Energies 398 8.4.3.5 Equations of Motion 400 8.4.3.6
Control Law 400 8.4.4 Summary 408 8.5 Magnetic Damping Treatments 410 8.5.1
Magnetic Constrained Layer Damping Treatments 410 8.5.2 Analysis of
Magnetic Constrained Layer Damping Treatments 412 8.5.2.1 Equation of
Motion 412 8.5.2.2 Response of the MCLD Treatment 414 8.5.3 Passive
Magnetic Composites 415 8.5.3.1 Concept of Passive Magnetic Composite
Treatment 417 8.5.3.2 Finite Element Modeling of Beams with PMC Treatment
417 8.5.4 Summary 430 8.6 Negative Stiffness Composites 430 8.6.1
Motivation to Negative Stiffness Composites 431 8.6.1.1 Sinusoidal
Excitation 431 8.6.1.2 Impact Loading 436 8.6.1.3 Magnetic Composite with
Negative Stiffness Inclusions 438 8.7 Summary 445 References 445 9
Vibration Damping with Shunted Piezoelectric Networks 469 9.1 Introduction
469 9.2 Shunted Piezoelectric Patches 469 9.2.1 Basics of Piezoelectricity
469 9.2.1.1 Effect of Electrical Boundary Conditions 471 9.2.1.2 Effect of
Mechanical Boundary Conditions 471 9.2.2 Basics of Shunted Piezo-Networks
472 9.2.2.1 Resistive-Shunted Circuit 474 9.2.2.2 Resistive and Inductive
Shunted Circuit 475 9.2.2.3 Resistive, Capacitive, and Inductive Shunted
Circuit 477 9.2.3 Electronic Synthesis of Inductances and Negative
Capacitances 479 9.2.3.1 Synthesis of Inductors 479 9.2.3.2 Synthesis of
Negative Capacitances 480 9.2.4 Why Negative Capacitance Is Effective? 480
9.2.5 Effectiveness of the Negative Capacitance from a Control System
Perspective 482 9.2.6 Electrical Analogy of Shunted Piezoelectric Networks
485 9.3 Finite Element Modeling of Structures Treated with Shunted
Piezo-Networks 487 9.3.1 Equivalent Complex Modulus Approach of Shunted
Piezo-Networks 487 9.3.2 Coupled Electromechanical Field Approach of
Shunted Piezo-Networks 491 9.4 Active Shunted Piezoelectric Networks 496
9.4.1 Basic Configurations 496 9.4.2 Dynamic Equations 498 9.4.2.1
Short-Circuit Configuration 498 9.4.2.2 Open-Circuit Configuration 498
9.4.2.3 Resistive-Shunted Configuration 498 9.4.3 More on the Resistive
Shunting Configuration 498 9.4.4 Open-Circuit to Resistive Shunting (OC-RS)
Configuration 500 9.4.4.1 Dynamic Equations 500 9.4.4.2 Switching Between
OC and RS Modes 500 9.4.5 Energy Dissipation of Different Shunting
Configurations 503 9.4.5.1 Energy Dissipation with Resistive Shunting 503
9.4.5.2 Energy Dissipation with OC-RS Switched Shunting 503 9.5 Multi-Mode
Vibration Control with Shunted Piezoelectric Networks 504 9.5.1 Multi-Mode
Shunting Approaches 504 9.5.2 Parameters of Behrens et al.'s Multi-Mode
Shunting Network 507 9.5.2.1 Components of the Current Flowing Branches 507
9.5.2.2 Components of the Shunting Branches 507 9.6 Summary 510 References
511 10 Vibration Control with Periodic Structures 523 10.1 Introduction 523
10.2 Basics of Periodic Structures 524 10.2.1 Overview 524 10.2.2 Transfer
Matrix Method 525 10.2.2.1 The Transfer Matrix 525 10.2.2.2 Basic
Properties of the Transfer Matrix 526 10.3 Filtering Characteristics of
Passive Periodic Structures 533 10.3.1 Overview 533 10.3.2 Periodic Rods in
Longitudinal Vibrations 534 10.4 Natural Frequencies, Mode Shapes, and
Response of Periodic Structures 535 10.4.1 Natural Frequencies and Response
535 10.4.2 Mode Shapes 539 10.5 Active Periodic Structures 541 10.5.1
Modeling of Active Periodic Structures 543 10.5.2 Dynamics of One Cell 543
10.5.2.1 Dynamics of the Passive Sub-Cell 543 10.5.2.2 Dynamics of the
Active Sub-Cell 543 10.5.2.3 Dynamics of the Entire Cell 545 10.5.2.4
Dynamics of the Entire Periodic Structure 546 10.6 Localization
Characteristics of Passive and Active Aperiodic Structures 549 10.6.1
Overview 549 10.6.2 Localization Factor 550 10.7 Periodic Rod with Periodic
Shunted Piezoelectric Patches 559 10.7.1 Transfer Matrix of a Plain Rod
Element 559 10.7.2 Transfer Matrix of a Rod/Piezo-Patch Element 560 10.7.3
Transfer Matrix of a Unit Cell 561 10.8 Two-Dimensional Active Periodic
Structure 562 10.8.1 Dynamics of Unit Cell 562 10.8.2 Formulation of Phase
Constant Surfaces 566 10.8.3 Filtering Characteristics 568 10.9 Periodic
Structures with Internal Resonances 569 10.9.1 Dynamics of Conventional
Periodic Structure 570 10.9.2 Dynamics of Periodic Structure with Internal
Resonances 572 10.9.2.1 Equivalent Mass. Of the Mass-In-Mass Arrangement
572 10.9.2.2 Transfer Matrix of the Mass-In-Mass Arrangement 572 10.10
Summary 578 References 578 11 Nanoparticle Damping Composites 589 11.1
Introduction 589 11.2 Nanoparticle-Filled Polymer Composites 590 11.2.1
Composites with Unidirectional Inclusions 591 11.2.2 Arbitrarily Oriented
Inclusion Composites 599 11.3 Comparisons with Classical Filler
Reinforcement Methods 607 11.4 Applications of Carbon Black/Polymer
Composites 614 11.4.1 Basic Physical Characteristics 614 11.4.2 Modeling of
the Piezo-Resistance of CB/Polymer Composites 617 11.4.3 The
Piezo-Resistivity of CB/Polymer Composites 619 11.5 CB/Polymer Composite as
a Shunting Resistance of Piezoelectric Layers 620 11.5.1 Finite Element
Model 620 11.5.2 Condensed Model of a Unit Cell 624 11.6 Hybrid Composites
with Shunted Piezoelectric Particles 629 11.6.1 Composite Description and
Assumptions 629 11.6.2 Shunted Piezoelectric Inclusions 631 11.6.3 Typical
Performance Characteristics of Hybrid Composites 631 11.7 Summary 636
References 636 12 Power Flow in Damped Structures 651 12.1 Introduction 651
12.2 Vibrational Power 651 12.2.1 Basic Definitions 651 12.2.2 Relationship
to System Energies 652 12.2.3 Basic Characteristics of the Power Flow 653
12.3 Vibrational Power Flow in Beams 656 12.4 Vibrational Power of Plates
661 12.4.1 Basic Equations of Vibrating Plates 661 12.4.2 Power Flow and
Structural Intensity 662 12.4.3 Control of the Power Flow and Structural
Intensity 668 12.4.4 Power Flow and Structural Intensity for Plates with
Passive and Active Constrained Layer Damping Treatments 671 12.5 Power Flow
and Structural Intensity for Shells 679 12.6 Summary 682 References 682
Glossary 699 Appendix 703 Index 715