Active and Passive Vibration Damping

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.

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 1.3 Summary 9 2 Viscoelastic Damping 11 2.1 Introduction 11 2.2 Classical Models of Viscoelastic Materials 11 2.3 Creep Compliance and Relaxation Modulus 20 2.4 Characteristics of the VEM in the Frequency Domain 25 2.5 Hysteresis and Energy Dissipation Characteristics of Viscoelastic Materials 27 2.6 Fractional Derivative Models of Viscoelastic Materials 32 2.7 Viscoelastic versus Other Types of Damping Mechanisms 38 2.8 Summary 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 3.4 Master Curves of Viscoelastic Materials 68 3.5 Time-Domain Measurement Techniques of the Dynamic Properties of Viscoelastic Materials 72 3.6 Summary 115 4 Viscoelastic Materials 127 4.1 Introduction 127 4.2 Golla–Hughes–McTavish (GHM) Model 127 4.3 Structural Finite Element Models of Beams Treated with VEM 150 4.4 Generalized Maxwell Model (GMM) 155 4.5 Augmenting Thermodynamic Field (ATF) Model 163 4.6 Fractional Derivative (FD) Models 167 4.7 Finite Element Modeling of Plates Treated with Passive Constrained Layer Damping 176 4.8 Finite Element Modeling of Shells Treated with Passive Constrained Layer Damping 185 4.9 Summary 192 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 5.4 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 5.7 Summary 234 6 Energy Dissipation in Damping Treatments 243 6.1 Introduction 243 6.2 Passive Damping Treatments of Rods 243 6.3 Active Constrained Layer Damping Treatments of Rods 251 6.4 Passive Constrained Layer Damping Treatments of Beams 257 6.5 Active Constrained Layer Damping Treatments of Beams 264 6.6 Passive and Active Constrained Layer Damping Treatments of Plates 267 6.7 Passive and Active Constrained Layer Damping Treatments of Axi-Symmetric Shells 274 6.8 Summary 288 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 7.3 Active Constrained Layer Damping for Beams 316 7.4 Active Constrained Layer Damping for Plates 336 7.5 Active Constrained Layer Damping for Shells 344 7.6 Summary 348 8 Advanced Damping Treatments 361 8.1 Introduction 361 8.2 Stand-Off Damping Treatments 362 8.3 Functionally Graded Damping Treatments 375 8.4 Passive and Active Damping Composite Treatments 390 8.5 Magnetic Damping Treatments 410 8.6 Negative Stiffness Composites 430 8.7 Summary 445 9 Vibration Damping with Shunted Piezoelectric Networks 469 9.1 Introduction 469 9.2 Shunted Piezoelectric Patches 469 9.3 Finite Element Modeling of Structures Treated with Shunted Piezo-Networks 487 9.4 Active Shunted Piezoelectric Networks 496 9.5 Multi-Mode Vibration Control with Shunted Piezoelectric Networks 504 9.6 Summary 510 10 Vibration Control with Periodic Structures 523 10.1 Introduction 523 10.2 Basics of Periodic Structures 524 10.3 Filtering Characteristics of Passive Periodic Structures 533 10.4 Natural Frequencies, Mode Shapes, and Response of Periodic Structures 535 10.5 Active Periodic Structures 541 10.6 Localization Characteristics of Passive and Active Aperiodic Structures 549 10.7 Periodic Rod with Periodic Shunted Piezoelectric Patches 559 10.8 Two-Dimensional Active Periodic Structure 562 10.9 Periodic Structures with Internal Resonances 569 10.10 Summary 578 11 Nanoparticle Damping Composites 589 11.1 Introduction 589 11.2 Nanoparticle-Filled Polymer Composites 590 11.3 Comparisons with Classical Filler Reinforcement Methods 607 11.4 Applications of Carbon Black/Polymer Composites 614 11.5 CB/Polymer Composite as a Shunting Resistance of Piezoelectric Layers 620 11.6 Hybrid Composites with Shunted Piezoelectric Particles 629 11.7 Summary 636 12 Power Flow in Damped Structures 651 12.1 Introduction 651 12.2 Vibrational Power 651 12.3 Vibrational Power Flow in Beams 656 12.4 Vibrational Power of Plates 661 12.5 Power Flow and Structural Intensity for Shells 679 12.6 Summary 682 References 682 Glossary 699 Appendix 703 Index 715