Vibrations

This new edition explains how vibrations can be used in a broad spectrum of applications and how to meet the challenges faced by engineers and system designers. The text integrates linear and nonlinear systems, and covers the time domain and the frequency domain, responses to harmonic and transient excitations, and discrete and continuous system models. It focuses on modeling, analysis, prediction, and measurement to provide a complete understanding of the underlying physical vibratory phenomena and their relevance for engineering design. Knowledge is put into practice through numerous examples with real-world applications in a range of disciplines, detailed design guidelines applicable to various vibratory systems, and over forty online interactive graphics which provide a visual summary of system behaviors and enable students to carry out their own parametric studies. Some thirteen new tables act as a quick reference for self-study, detailing key characteristics of physical systems and summarizing important results. This is an essential text for undergraduate and graduate courses in vibration analysis, and a valuable reference for practicing engineers. Contents......Page 5 List of Examples......Page 11 List of Interactive Graphics......Page 14 List of Symbols......Page 16 Preface to the Third Edition......Page 22 1.1 Introduction......Page 28 1.2 A Brief History of Vibrations......Page 33 1.3 About This Book......Page 35 2.1 Introduction......Page 38 2.2 Inertia Elements......Page 40 2.3.1 Introduction......Page 45 2.3.2 Linear Springs......Page 47 2.3.3 Nonlinear Springs......Page 59 2.3.4 Other Forms of Potential Energy Elements......Page 65 2.4.1 Viscous Damping......Page 71 2.4.2 Combinations of Viscous Dampers and Linear Springs......Page 76 2.4.3 Other Forms of Dissipation......Page 79 2.5.2 A Few Simple Models......Page 82 2.5.3 A Microelectromechanical System......Page 87 2.5.4 The Human Body......Page 89 2.5.5 A Ski......Page 90 2.5.6 Cutting Process......Page 91 2.6 Design for Vibration......Page 92 2.7 Summary......Page 93 Exercises......Page 94 3.1 Introduction......Page 103 3.2.1 Force-Balance Methods......Page 104 3.2.2 Moment-Balance Methods......Page 110 3.3.1 Natural Frequency......Page 114 3.3.2 Damping Factor......Page 119 3.4 Governing Equations for Different Types of Damping......Page 123 3.5.1 System with Base Excitation......Page 124 3.5.2 System with Unbalanced Rotating Mass......Page 126 3.5.3 System with Added Mass Due to a Fluid......Page 127 3.6 Lagrange’s Equations......Page 129 3.7 Summary of Natural Frequency Equations for Single Degree-of-Freedom Systems......Page 156 3.8 Summary......Page 162 Exercises......Page 163 4.1 Introduction......Page 175 4.2.1 Introduction: Damping Cases......Page 177 4.2.2 Free Response of Underdamped Systems: Kelvin–Voigt Model......Page 184 4.2.3 Free Response of Underdamped Systems: Maxwell Model......Page 203 4.3 Stability of a Single Degree-of-Freedom System......Page 205 4.4.1 Nonlinear Stiffness......Page 209 4.4.2 Nonlinear Damping......Page 213 4.5 Summary......Page 214 Exercises......Page 216 5.1 Introduction......Page 224 5.2.1 Excitation Applied from t = 0......Page 227 5.2.2 Excitation Present for All Time......Page 237 5.2.3 Response of Undamped System and Resonance......Page 241 5.2.4 Magnitude and Phase Information: Mass Excitation......Page 244 5.2.5 Magnitude and Phase Information: Rotating Unbalanced Mass......Page 248 5.2.6 Magnitude and Phase Information: Base Excitation......Page 253 5.2.7 Summary of Results of Sections 5.2.4, 5.2.5, and 5.2.6......Page 257 5.2.8 Harmonic Excitation of a System with a Maxwell Model......Page 260 5.3 Response to Excitation with Harmonic Components......Page 265 5.4.1 Introduction......Page 275 5.4.2 Curve Fitting and Parameter Estimation......Page 276 5.4.3 Amplitude Response Function and Filter Characteristics......Page 277 5.4.4 Relationship of the Frequency-Response Function to the Transfer Function......Page 282 5.4.5 Alternative Forms of the Frequency-Response Function......Page 286 5.5 Acceleration Measurement: Accelerometer......Page 288 5.6 Vibration Isolation......Page 290 5.7 Energy Dissipation and Equivalent Damping......Page 297 5.8 Influence of Nonlinear Stiffness on Forced Response......Page 309 5.9 Summary......Page 316 Exercises......Page 317 6.1 Introduction......Page 324 6.2 Response to Impulse Excitation......Page 327 6.3 Response to Step Input Excitation......Page 337 6.4 Response to Rectangular Pulse Excitation......Page 343 6.5 Response to Other Excitation Waveforms......Page 349 6.5.1 Significance of the Spectral Content of the Applied Force: An Example......Page 361 6.6 Impact Testing......Page 365 6.7 Summary......Page 367 Exercises......Page 368 7.1 Introduction......Page 371 7.2.1 Force-Balance and Moment-Balance Methods......Page 373 7.2.2 General Form of Equations for a Linear Multi-Degree-of-Freedom System......Page 383 7.2.3 Lagrange’s Equations of Motion......Page 386 7.3.1 Undamped Systems: Natural Frequencies and Mode Shapes......Page 405 7.3.3 Undamped Systems: Properties of Mode Shapes......Page 429 7.3.4 Characteristics of Damped Systems......Page 438 7.3.5 Conservation of Energy......Page 448 7.4 Rotating Shafts on Flexible Supports......Page 450 7.5 Stability......Page 461 7.6 Summary......Page 468 Exercises......Page 469 8.1 Introduction......Page 485 8.2.1 General Solution......Page 487 8.2.2 Response to Initial Conditions......Page 492 8.3 Response to Arbitrary Forcing and Initial Conditions: Direct Numerical Approach......Page 499 8.4.1 Frequency-Response Function......Page 502 8.5.1 Undamped Vibration Absorber......Page 516 8.5.2 Damped Linear Vibration Absorber......Page 519 8.5.3 Centrifugal Pendulum Vibration Absorber......Page 531 8.5.4 Bar Slider System......Page 535 8.5.5 Pendulum Absorber......Page 538 8.5.6 Particle Impact Damper......Page 542 8.6 Vibration Isolation: Transmissibility Ratio......Page 552 8.7 Systems with Moving Base......Page 563 8.8 Summary......Page 565 Exercises......Page 566 9.1 Introduction......Page 572 9.2 Governing Equations of Motion......Page 574 9.2.1 Preliminaries from Solid Mechanics......Page 575 9.2.2 Potential Energy, Kinetic Energy, and Work......Page 577 9.2.3 Derivation of the Equations of Motion......Page 584 9.2.4 Beam Equations for a General Case......Page 586 9.3.1 Introduction......Page 593 9.3.2 General Solution for Natural Frequencies and Mode Shapes for Beams with Constant Cross-Section......Page 597 9.3.3 Orthogonality of the Mode Shapes......Page 607 9.3.4 Natural Frequencies and Mode Shapes of Constant Cross-Section Beams Without In-Span Attachments: Effects of Boundary Conditions......Page 610 9.3.5 Effects of Stiffness and Inertial Elements Attached at an Interior Location......Page 626 9.3.6 Effects of an Axial Force and an Elastic Foundation on the Natural Frequency......Page 643 9.3.7 Tapered Beams......Page 644 9.4 Forced Oscillations......Page 649 9.5 Summary......Page 666 Exercises......Page 667 Appendices......Page 10 A Preliminaries from Dynamics......Page 674 B Laplace Transform Pairs......Page 688 C Solutions to Ordinary Differential Equations......Page 696 D Matrices......Page 706 E Complex Numbers and Variables......Page 710 F State-Space Formulation......Page 715 G Natural Frequencies and Mode Shapes of Bars, Shafts, and Strings......Page 722 H Evaluation of Eq. (9.120)......Page 732 Answers to Selected Exercises......Page 735 Glossary......Page 741 Index......Page 746 "Vibrations: This new edition explains how vibrations can be used in a broad spectrum of applications and how to meet the challenges faced by engineers and system designers. The text integrates linear and nonlinear systems and covers the time domain and the frequency domain, responses to harmonic and transient excitations, and discrete and continuous system models. It focuses on modeling, analysis, prediction, and measurement to provide a complete understanding of the underlying physical vibratory phenomena and their relevance for engineering design"-- Provided by publisher An introduction to the modeling, analysis, design, and measurement of vibrations, and their real-world applications. With examples and homework problems throughout, and lecture slides, a solutions manual, and unique interactive graphics available online, this is an essential text for undergraduate and graduate courses in vibration analysis.