Vibrations, Second Edition

Front Cover......Page 1
Title Page......Page 2
Copyright......Page 3
Contents......Page 4
1.1 Introduction......Page 22
1.2.1 Kinematics of Particles and Rigid Bodies......Page 25
1.2.2 Generalized Coordinates and Degrees of Freedom......Page 34
1.2.3 Particle and Rigid-Body Dynamics......Page 36
1.2.4 Work and Energy......Page 39
Exercises......Page 40
2.1 Introduction......Page 44
2.2 Inertia Elements......Page 45
2.3.1 Introduction......Page 49
2.3.2 Linear Springs......Page 52
2.3.3 Nonlinear Springs......Page 63
2.3.4 Other Forms of Potential Energy Elements......Page 66
2.4 Dissipation Elements......Page 70
2.4.1 Viscous Damping......Page 71
2.4.2 Other Forms of Dissipation......Page 74
2.5.1 Introduction......Page 75
2.5.2 A Microelectromechanical System......Page 76
2.5.3 The Human Body......Page 77
2.5.4 A Ski......Page 79
2.5.5 Cutting Process......Page 80
2.6 Design for Vibration......Page 81
Exercises......Page 82
3.1 Introduction......Page 90
3.2.1 Force-Balance Methods......Page 91
3.2.2 Moment-Balance Methods......Page 97
3.3 Natural Frequency and Damping Factor......Page 100
3.3.1 Natural Frequency......Page 101
3.3.2 Damping Factor......Page 104
3.4 Governing Equations for Different Types of Damping......Page 109
3.5.1 System with Base Excitation......Page 110
3.5.2 System with Unbalanced Rotating Mass......Page 111
3.5.3 System with Added Mass Due to a Fluid......Page 113
3.6 Lagrange’s Equations......Page 114
3.7 Summary......Page 137
Exercises......Page 138
4.1 Introduction......Page 148
4.2.1 Introduction......Page 150
4.2.2 Initial Velocity......Page 157
4.2.3 Initial Displacement......Page 175
4.2.4 Initial Displacement and Initial Velocity......Page 179
4.3 Stability of a Single Degree-of-Freedom System......Page 182
4.4 Machine Tool Chatter......Page 186
4.5.1 Nonlinear Stiffness......Page 189
4.5.2 Nonlinear Damping......Page 192
Exercises......Page 195
5.1 Introduction......Page 202
5.2.1 Excitation Applied from t = 0......Page 204
5.2.2 Excitation Present for All Time......Page 213
5.2.3 Response of Undamped System and Resonance......Page 217
5.2.4 Magnitude and Phase Information......Page 219
5.3.1 Introduction......Page 225
5.3.2 Curve Fitting and Parameter Estimation......Page 226
5.3.3 Sensitivity to System Parameters and Filter Characteristics......Page 229
5.3.4 Relationship of the Frequency-Response Function to the Transfer Function......Page 235
5.3.5 Alternative Forms of the Frequency-Response Function......Page 238
5.4 System with Rotating Unbalanced Mass......Page 239
5.5 System with Base Excitation......Page 246
5.6 Acceleration Measurement: Accelerometer......Page 256
5.7 Vibration Isolation......Page 259
5.8 Energy Dissipation and Equivalent Damping......Page 265
5.9 Response to Excitation with Harmonic Components......Page 276
5.10 Influence of Nonlinear Stiffness on Forced Response......Page 290
Exercises......Page 298
6.1 Introduction......Page 306
6.2 Response to Impulse Excitation......Page 308
6.3 Response to Step Input......Page 321
6.4 Response to Ramp Input......Page 331
6.5 Spectral Energy of the Response......Page 337
6.6 Response to Rectangular Pulse Excitation......Page 338
6.7 Response to Half-Sine Wave Pulse......Page 343
6.8 Impact Testing......Page 353
Exercises......Page 354
7.1 Introduction......Page 358
7.2 Governing Equations......Page 359
7.2.1 Force-Balance and Moment-Balance Methods......Page 360
7.2.2 General Form of Equations for a Linear Multi-Degree-of-Freedom System......Page 370
7.2.3 Lagrange’s Equations of Motion......Page 372
7.3.1 Undamped Systems: Natural Frequencies and Mode Shapes......Page 390
7.3.2 Undamped Systems: Properties of Mode Shapes......Page 414
7.3.3 Characteristics of Damped Systems......Page 419
7.3.4 Conservation of Energy......Page 429
7.4 Rotating Shafts On Flexible Supports......Page 430
7.5 Stability......Page 440
Exercises......Page 443
8.1 Introduction......Page 456
8.2.1 General Solution......Page 459
8.2.2 Response to Initial Conditions......Page 463
8.2.3 Response to Harmonic Forcing and the Frequency-Response Function......Page 469
8.3 State-Space Formulation......Page 479
8.4 Laplace Transform Approach......Page 492
8.4.1 Response to Arbitrary Forcing......Page 494
8.4.2 Response to Initial Conditions......Page 496
8.4.3 Force Transmitted to a Boundary......Page 501
8.5 Transfer Functions and Frequency-Response Functions......Page 502
8.6 Vibration Absorbers......Page 516
8.6.1 Linear Vibration Absorber......Page 517
8.6.2 Centrifugal Pendulum Vibration Absorber......Page 528
8.6.3 Bar Slider System......Page 531
8.6.4 Pendulum Absorber......Page 534
8.6.5 Particle Impact Damper......Page 538
8.7 Vibration Isolation: Transmissibility Ratio......Page 546
8.8 Systems with Moving Base......Page 551
8.9 Summary......Page 555
Exercises......Page 556
9.1 Introduction......Page 562
9.2.1 Preliminaries from Solid Mechanics......Page 564
9.2.2 Potential Energy, Kinetic Energy, and Work......Page 567
9.2.3 Extended Hamilton’s Principle and Derivation of Equations of Motion......Page 571
9.2.4 Beam Equation for a General Case......Page 575
9.3.1 Introduction......Page 583
9.3.2 Natural Frequencies, Mode Shapes, and Orthogonality of Modes......Page 587
9.3.3 Effects of Boundary Conditions......Page 595
9.3.4 Effects of Stiffness and Inertial Elements Attached at an Interior Location......Page 609
9.3.5 Beams with an Interior Mass, Spring, and Single Degree-of-Freedom System Attached Simultaneously......Page 634
9.3.6 Effects of an Axial Force and an Elastic Foundation on the Natural Frequency......Page 646
9.3.7 Tapered Beams......Page 648
9.4 Forced Oscillations......Page 653
9.5 Summary......Page 669
Glossary......Page 670
A: Laplace Transform Pairs......Page 674
B: Fourier Series......Page 681
C: Decibel Scale......Page 682
D: Solutions to Ordinary Differential Equations......Page 684
E: Matrices......Page 696
F: Complex Numbers and Variables......Page 700
G: Natural Frequencies and Mode Shapes of Bars, Shafts, and Strings......Page 704
Answers to Selected Exercises......Page 714
Index......Page 722