Harris' Shock and Vibration Handbook

Preface......Page 5
Table of Contents......Page 7
Concepts of Shock and Vibration......Page 12
Control of Shock and Vibration......Page 13
Content of Handbook......Page 14
Symbols and Acronyms......Page 16
Characteristics of Harmonic Motion......Page 18
Appendix 1.1 Natural Frequencies of Commonly Used Systems......Page 20
Appendix 1.2 Terminology......Page 27
Translational Motion......Page 39
Rotational Motion......Page 40
Free Vibration without Damping......Page 41
Free Vibration with Viscous Damping......Page 43
Forced Vibration......Page 45
Forced Vibration without Damping......Page 46
Forced Vibration with Viscous Damping......Page 47
Degrees-of-Freedom......Page 57
Stiffness Coefficients......Page 58
Free Vibration......Page 59
Forced Motion......Page 61
Uniform Viscous Damping......Page 65
Uniform Mass Damping......Page 67
Lagrangian Equations......Page 68
System of Coordinates......Page 71
Equations of Small Motion of a Rigid Body......Page 72
Mass......Page 73
Center-of-Mass......Page 84
Moment and Product of Inertia......Page 85
Properties of Resilient Supports......Page 92
Equations of Motion for a Resiliently Supported Rigid Body......Page 93
One Plane of Symmetry with Orthogonal Resilient Supports......Page 97
Two Planes of Symmetry with Orthogonal Resilient Supports......Page 99
Three Planes of Symmetry with Orthogonal Resilient Supports......Page 106
Two Planes of Symmetry with Resilient Supports Inclined in One Plane Only......Page 108
Complete Decoupling of Modes Using Radially Inclined Resilient Supports......Page 110
Foundation-Induced Sinusoidal Vibration......Page 112
Body-Induced Sinusoidal Vibration......Page 117
Foundation-Induced Velocity Shock......Page 121
References......Page 126
Introduction......Page 127
Simple Spring-Mass System......Page 128
Stretched String with Concentrated Mass......Page 129
Belt Friction System......Page 130
Systems with Asymmetric Stiffness......Page 131
Free Vibration......Page 132
Response Curves for Forced Vibration of Systems with Symmetric Stiffness......Page 133
Response Curves for Forced Vibration of Systems with Asymmetric Stiffness......Page 135
Other Phenomena......Page 143
Exact Solutions......Page 144
Free Vibration......Page 145
Forced Vibration......Page 147
Chaotic Dynamics......Page 148
Duffing's Method......Page 149
Rauscher's Method......Page 150
The Perturbation Method......Page 151
The Method of Kryloff and Bogoliuboff......Page 152
The Ritz Method......Page 154
System with Linear Damping and General Restoring Forces......Page 157
Graphical Methods of Integration......Page 159
Phase-Plane Integration of Stepwise Linear Systems......Page 161
Phase-Plane Integration of Autonomous Systems with Nonlinear Damping......Page 163
Generalized Phase-Plane Analysis......Page 165
Stability of Periodic Nonlinear Vibration......Page 166
References......Page 170
Introduction......Page 172
Analytic Modeling......Page 173
General Description......Page 175
Hysteretic Whirl......Page 176
Whirl Due to Fluid Trapped in Rotor......Page 180
Dry Friction Whip......Page 182
Seal and Blade-Tip-Clearance Effect in Turbomachinery......Page 183
Propeller and Turbomachinery Whirl......Page 186
Lateral Instability Due to Asymmetric Shafting......Page 187
Lateral Instability Due to Pulsating Torque......Page 188
Lateral Instability Due to Pulsating Longitudinal Loads......Page 189
Stick-Slip Rubs and Chatter......Page 190
Bistable Vibration......Page 191
Unstable Imbalance......Page 192
References......Page 194
Forms of Dynamic Absorbers and Auxiliary Mass Dampers......Page 197
Ways of Expressing the Effects of Auxiliary Mass Systems......Page 198
The Influence of a Simple Auxiliary Mass System Upon a Vibrating System......Page 200
The Dynamic Absorber......Page 203
Auxiliary Mass Dampers......Page 205
Effect of Nonlinearity in the Spring of an Auxiliary Mass Damper......Page 215
Distributed Mass Absorbers......Page 217
The Dynamic Absorber......Page 220
Reduction of Roll of Ships by Auxiliary Tanks......Page 221
Reduction of Roll of Ships by Gyroscopes......Page 222
Auxiliary Mass Dampers Applied to Rotating Machinery......Page 223
Auxiliary Mass Dampers Applied to Torsional Vibration......Page 225
Dynamic Absorbers Tuned to Orders of Vibration Rather than Constant Frequencies......Page 227
Applications of Dampers to Multiple Degree-of-Freedom Systems......Page 233
Activated Vibration Absorbers......Page 234
The Use of Auxiliary Mass Devices to Reduce Transient and Self-Excited Vibrations......Page 235
References......Page 238
Free Vibration......Page 239
Longitudinal and Torsional Vibrations of Uniform Circular Rods......Page 244
Lateral Vibration of Straight Beams......Page 249
Lateral Vibration of Beams with Masses Attached......Page 263
Lateral Vibration of Plates......Page 266
Transfer Matrix Method......Page 278
Classical Solution......Page 281
Method of Virtual Work......Page 283
Vibration Resulting from Motion of Support......Page 285
References......Page 286
Introduction......Page 289
Differential Equation of Motion......Page 290
Methods of Solution of the Differential Equation......Page 291
Initial Conditions of the System......Page 303
Step-Type Excitation Functions......Page 304
Pulse-Type Excitation Functions......Page 310
Summary of Transient Response Spectra for the Single Degree-of-Freedom, Linear, Undamped System......Page 337
Single Degree-of-Freedom Linear System with Damping......Page 339
Damping Forces Proportional to Velocity (Viscous Damping)......Page 340
Constant (Coulomb) Damping Forces; Phase-Plane Method......Page 342
Phase-Plane-Delta Method......Page 343
Multiple Degree-of-Freedom, Linear, Undamped Systems......Page 345
General Investigation of Transients......Page 346
References......Page 347
Direct Central Impact of Two Spheres......Page 348
Hertz Theory of Impact of Two Solid Spheres......Page 349
Impact of a Solid Sphere on an Elastic Plate......Page 350
Transverse Impact of a Mass on a Beam......Page 352
Impact of a Rigid Body on a Damped Elastically Supported Beam......Page 353
Plastic Deformation Resulting from Impact......Page 357
References......Page 359
Mechanical Impedance of Vibratory Systems......Page 361
Basic Mechanical Elements......Page 362
Combinations of Mechanical Elements......Page 364
Kirchhoff's Laws......Page 366
Superposition Theorem......Page 368
Norton's Equivalent System......Page 369
Mechanical 2-Ports......Page 370
Measurements......Page 371
Applications......Page 372
References......Page 374
Random Vibration Analysis......Page 375
Probability Distribution Functions......Page 377
Moments of the Probability Distribution......Page 379
Gaussian (Normal) Distribution......Page 380
Correlation Functions......Page 381
Power Spectral Density......Page 382
Response of a Single Degree-of-Freedom System......Page 384
Response of Multiple Degree-of-Freedom Systems......Page 386
Level Crossings......Page 388
Cumulative Damage......Page 389
Statistical Energy Analysis......Page 390
Sea Modeling of Systems......Page 392
Mode Counts......Page 397
Damping Loss Factors......Page 399
Coupling Loss Factors......Page 400
Modal Excitations......Page 402
System Response Distribution......Page 403
Transient (Shock) Response Using Sea......Page 405
References......Page 406
Introduction......Page 407
Mass-Spring Transducers (Seismic Transducers)......Page 408
Acceleration-Measuring Transducers......Page 410
Accelerometer Requirements for Shock......Page 411
Resolution......Page 416
Amplitude Linearity and Limits......Page 417
Frequency Range......Page 418
Environmental Effects......Page 420
Principle of Operation......Page 421
Typical Piezoelectric Accelerometer Constructions......Page 424
Physical Characteristics of Piezoelectric Accelerometers......Page 426
Electrical Characteristics of Piezoelectric Accelerometers......Page 427
Low-Impedance Piezoelectric Accelerometers Containing Internal Electronics......Page 428
Effects of Temperature......Page 429
Principle of Operation......Page 430
Typical Piezoresistive Accelerometer Constructions......Page 431
Electrical Characteristics of Piezoresistive Accelerometers......Page 433
Force Gages......Page 436
Force-Gage Characteristics......Page 437
Laser Doppler Vibrometers......Page 438
Displacement Measurement System......Page 440
Fiber-Optic Reflective Displacement Sensor......Page 441
Differential-Transformer Pickups......Page 442
Servo Accelerometer......Page 443
Displacement Transducer (Proximity Probe)......Page 444
Variable-Capacitance-Type Accelerometer......Page 445
References......Page 446
Accelerometer Preamplifiers......Page 447
Detectors......Page 451
Vibration Meters......Page 456
Tape Recorders......Page 457
Analog-to-Digital Converters......Page 459
Antialiasing Filters......Page 460
Digital-to-Analog Conversion......Page 462
References......Page 463
Introduction......Page 464
Electrical Filters......Page 465
FFT Analyzers......Page 474
Analysis of Stationary Signals Using FFT......Page 484
Analysis of Nonstationary Signals......Page 491
Related Analysis Techniques......Page 497
References......Page 505
Measurement Planning......Page 506
Selecting the Transducer......Page 509
Transducer Mountings......Page 510
Transducers......Page 518
Overall System......Page 519
Cable and Wiring Considerations......Page 523
Cable Noise Generation......Page 524
Noise-Suppression Techniques......Page 525
Data Sheets for Logging Test Information......Page 527
References......Page 528
Introduction......Page 529
Types of Condition Monitoring Systems......Page 530
Establishing a Condition Monitoring Program......Page 531
Fault Detection in Rotating Machinery......Page 533
How Spectrum Changes Are Related to the Condition of a Machine......Page 534
Subsynchronous Components......Page 536
Harmonics of the Power Line Frequency......Page 537
Sideband Patterns Due to Modulation......Page 542
Harmonic Patterns Not Harmonically Related to the Rotational Speed......Page 544
Envelope Detection......Page 545
Application of Cepstrum Analysis......Page 549
Application of Gated Vibration Analysis on Reciprocating Machines......Page 550
Trend Analysis......Page 551
References......Page 552
Introduction......Page 554
Transverse Sensitivity......Page 555
Temperature Effects......Page 556
Strain-Gage Selection Considerations......Page 557
Physical Environment......Page 558
Strain-Gage Measurements......Page 559
Displacement Measurement......Page 560
Velocity......Page 561
Pressure......Page 562
Strain-Gage Circuitry and Instrumentation......Page 564
Potentiometer Circuit......Page 565
Selection of Instruments for Strain Measurement......Page 566
References......Page 567
Pickup Sensitivity, Calibration Factor, and Frequency Response......Page 569
Calibration Traceability......Page 570
Comparison Methods of Calibration......Page 572
Reciprocity Method......Page 573
Calibration Using the Earth's Gravitational Field......Page 576
Centrifuge Calibrator......Page 577
Interferometer Calibrators......Page 578
Sinusoidal-Excitation Methods......Page 583
Shock-Excitation Methods......Page 584
Integration of Accelerometer Output......Page 587
Impact-Force Shock Calibrator......Page 588
Vibration Exciters Used for Calibration......Page 590
Mechanical Exciters......Page 591
Calibration of Transverse Sensitivity......Page 592
References......Page 594
Introduction......Page 597
Standards Activities......Page 598
Standards-Developing Organizations and Sources......Page 603
Environmental Specifications......Page 605
Shock and Vibration Environments......Page 606
Descriptions of Shock and Vibration Environments......Page 607
Development Tests......Page 608
Acceptance Tests......Page 609
Reliability Growth Tests......Page 610
Measurement or Prediction of Spectra......Page 611
Grouping of Measured or Predicted Spectra into Zones......Page 612
Determination of Zone Limits......Page 613
Selection of Final Test Levels......Page 615
Failure Models......Page 617
Compressing Time-Varying Service Environments......Page 618
Accelerated Tests......Page 619
Identification of Test Failures......Page 620
Types of Excitation......Page 621
Test Fixtures......Page 622
References......Page 623
Introduction......Page 625
Measurement Degrees-of-Freedom......Page 626
Basic Assumptions......Page 628
Modal Analysis Theory......Page 629
Single Degree-of-Freedom Systems......Page 630
Multiple Degree-of-Freedom Systems......Page 635
Experimental Modal Analysis Methods......Page 638
Modal Data Acquisition......Page 639
Digital Signal Processing......Page 640
Discrete Fourier Transform......Page 642
Test Environment Considerations......Page 643
Measurement Formulation......Page 644
Frequency Response Function Estimation......Page 645
Practical Measurement Considerations......Page 654
Modal Identification Concepts......Page 663
Modal Identification Algorithms (SDOF)......Page 685
Modal Identification Algorithms (MDOF)......Page 686
Measurement Synthesis......Page 690
Modal Vector Orthogonality......Page 691
Modal Vector Consistency......Page 692
Modal Complexity......Page 694
References......Page 695
Classifications of Vibration Data......Page 697
Overall Values......Page 699
Stationary Deterministic Vibrations......Page 700
Stationary Random Vibrations......Page 702
Nonstationary Deterministic Vibrations......Page 706
Nonstationary Random Vibrations......Page 707
Engineering Applications of Data Analysis......Page 709
Data Validation and Editing......Page 710
Data Storage......Page 711
Vibration Data Analysis Procedures......Page 712
Procedures for Stationary Deterministic Data Analysis......Page 713
Procedures for Stationary Random Data Analysis......Page 714
Procedures for Nonstationary Data Analysis......Page 720
References......Page 724
Basic Considerations......Page 725
Acceleration Impulse or Step Velocity......Page 727
Acceleration Step......Page 728
Decaying Sinusoidal Acceleration......Page 729
Data Reduction to the Frequency Domain......Page 730
Data Reduction to the Response Domain......Page 734
Shock Response Spectrum......Page 749
References......Page 750
Source of Ground Motion......Page 751
Response of Simple Structures to Ground Motions......Page 752
Earthquake Ground Motion......Page 755
Elastic Systems......Page 756
Design Response Spectra......Page 759
Response Spectra for Inelastic Systems......Page 761
Use of Response Spectra......Page 763
General Considerations......Page 764
Effects of Design on Behavior and on Analysis......Page 765
Design Lateral Forces......Page 767
Gravity Loads......Page 768
Simulation Testing......Page 769
Equipment and Lifelines......Page 770
Slip Damping......Page 0
Introduction......Page 773
Direct-Drive Mechanical Vibration Machines......Page 774
Prominent Features......Page 775
Circular-Motion Machine......Page 776
Rectilinear-Motion Machine......Page 777
Prominent Features......Page 778
General Description......Page 779
Induction-Type Shaker......Page 780
Frequency Response Considerations......Page 781
Characterization of an Electrodynamic Shaker as a Two-Port Network......Page 782
System Ratings......Page 784
Specifications......Page 785
Operating Principle......Page 788
Piezoelectric Vibration Exciters......Page 790
Impact Exciters......Page 791
Multiple Shakers Driving a Single Test Item......Page 792
Vibration Fixtures......Page 793
References......Page 794
Introduction......Page 795
Damage Potential and Shock Response Spectra......Page 796
Calibration......Page 797
Specifying a Shock Test......Page 798
Characteristic Types of Shocks......Page 799
Simple Shock Pulse Machines......Page 801
Complex Shock Pulse Machines......Page 804
Multiple-Impact Shock Machines......Page 807
References......Page 808
Introduction......Page 809
Comparison of Near-Field and Far-Field Characteristics......Page 810
Test Techniques for Near- and Far-Field Pyroshock......Page 812
Quantifying Pyroshock for Test Specification......Page 813
Measurement Techniques......Page 815
Pyrotechnically Excited Near-Field Simulation......Page 816
Mechanically Excited Far-Field Simulation......Page 818
References......Page 826
Introduction......Page 828
General Purpose......Page 829
Specialized Processors......Page 831
General-Purpose Programs......Page 837
Special-Purpose Applications......Page 840
Digital Shock and Vibration Data Analysis......Page 841
Digital Control Systems for Shock and Vibration Testing......Page 846
References......Page 861
Matrices......Page 864
Definitions......Page 865
Matrix Operations......Page 867
Quadratic Forms......Page 870
Formulation of Vibration Problems in Matrix Form......Page 872
Coupling of the Equations......Page 874
The Matrix Eigenvalue Problem......Page 875
Modal and Spectral Matrices......Page 876
Properties of the Solution......Page 877
Eigenvector Expansions......Page 878
Rayleigh's Quotient......Page 879
Free Vibration with Specified Initial Conditions......Page 881
Steady-State Forced Sinusoidal Vibration......Page 882
Response to General Excitation......Page 883
Complex Eigenvalue Problem......Page 884
Perturbation Approximation to Complex Eigenvalue Problem......Page 885
Formal Solutions......Page 886
Approximate Solutions......Page 888
References......Page 890
Application of Minimal Principles......Page 891
Typical Finite Elements......Page 894
Cut-Off Frequency and Grid Spacing......Page 898
Modal Density and Effectiveness of Finite Element Models......Page 899
Fundamental Dynamic Formulations......Page 900
Application of Normal Modes in Transient Dynamic Analysis......Page 901
Modal Truncation......Page 903
Applied Loads and Enforced Motions......Page 905
Strategies for Dealing with Large-Order Models......Page 907
Component Mode Synthesis Strategies......Page 910
Dynamic Response Resulting from Various Environments......Page 912
References......Page 914
Added Mass and Inertial Coupling......Page 916
Wave-Induced Vibration of Structures......Page 921
Vortex-Induced Vibration......Page 923
Fluid Elastic Instability......Page 929
Internal Flow in Pipes......Page 931
References......Page 934
Forms of Aerodynamic Excitation......Page 936
Basic Wind Characteristics......Page 939
Fundamentals of Response Prediction......Page 943
Gust-Factor Approach......Page 947
Effect of Gusts on Cladding and Windows......Page 949
Prediction of Vortex-Induced Oscillation......Page 950
Harmonic Excitation of Prismatic Cylinders by Vortices......Page 951
Random Excitation of Prismatic Cylinders by Vortices......Page 952
Random Excitation of Tapered Cylinders by Vortices......Page 954
Galloping Oscillations......Page 955
References......Page 959
Sound Sources......Page 962
Jet and Rocket Exhausts......Page 964
Propellers and Fans......Page 968
Turbulent Boundary Layer......Page 969
Linear Analysis......Page 971
Nonlinear Vibration......Page 976
Acoustic Fatigue......Page 978
Progressive Wave Tubes......Page 979
Reverberation Chambers......Page 980
References......Page 981
Concept of Vibration Isolation......Page 983
Form of Isolator......Page 984
Influence of Damping in Vibration Isolation......Page 987
Rigidly Connected Viscous Damper......Page 988
Rigidly Connected Coulomb Damper......Page 989
Elastically Connected Viscous Damper......Page 992
Elastically Connected Coulomb Damper......Page 994
System with Two Planes of Symmetry......Page 1000
Vibration Isolation in Coupled Modes......Page 1006
Inclined Isolators......Page 1011
Decoupling of Modes......Page 1012
Properties of a Biaxial Stiffness Isolator......Page 1013
Properties of Isolator with Respect to Arbitrarily Selected Axes......Page 1014
Influence Coefficient Transformation......Page 1016
Principal Influence Coefficients......Page 1017
Influence Coefficient Transformation from the Principal Axes......Page 1018
Nonlinear Vibration Isolators......Page 1020
Natural Frequency......Page 1021
References......Page 1025
Uncoupled Motions......Page 1026
Analogy Between Translation and Rotation......Page 1027
Classification of Shock Isolation Problems......Page 1028
Idealized Systems - Class I......Page 1029
Mathematical Equivalence of Class I and Class II Problems......Page 1030
Physical Basis for Velocity Step......Page 1031
General Form of Isolator Characteristics......Page 1032
Examples of Particular Isolator Characteristics......Page 1034
Response of Rigid Body System to Acceleration Pulse......Page 1041
Response to a Rectangular Pulse......Page 1042
Half-Sine Pulse......Page 1043
Comparison of Maximum Accelerations......Page 1044
Shock Response Spectrum......Page 1045
Impact with Rebound......Page 1047
Impact without Rebound......Page 1051
Equipment Rigidly Attached to Support......Page 1056
Equipment Shock Isolated......Page 1057
Types and Characteristics of Isolators......Page 1063
Elastomeric Isolators......Page 1064
Metal Springs......Page 1070
Air (Pneumatic) Springs......Page 1074
Isolators in Parallel......Page 1077
Important Factors Affecting Selection......Page 1078
How to Select Isolators......Page 1083
Examples......Page 1085
Avoiding Isolator Installation Problems......Page 1089
Shock and Vibration Isolator Specifications......Page 1090
An Active System for Resiliently Supporting a Body at Given Position Despite Variations in the Applied Load......Page 1091
An Active System for Controlling its System Resonance and Low-Frequency Vibration Isolation......Page 1093
References......Page 1103
Rubber Compounding......Page 1104
Elastomers......Page 1105
Anti-Degradents......Page 1106
Mixing......Page 1107
Stress-Strain......Page 1108
Tear......Page 1110
Low-Temperature Properties......Page 1111
Exposure to Ozone and Oxygen......Page 1112
Measurement of Dynamic Properties......Page 1113
Vibration Isolation and Damping......Page 1115
Fatigue Failure......Page 1118
References......Page 1120
Introduction......Page 1122
Static Properties......Page 1123
Temperature and Strain-Rate Effects......Page 1125
Critical Strain Velocity......Page 1128
Fatigue......Page 1129
Stress-Life Method......Page 1131
Strain-Life Method......Page 1136
Fracture Mechanics Method......Page 1137
Variable-Amplitude Loading......Page 1138
Cycle Counting......Page 1139
References......Page 1143
Basic Types of Composites......Page 1144
Continuous Fiber Composites......Page 1145
Special Design Issues and Opportunities......Page 1146
Composite Properties......Page 1149
In-Situ Properties......Page 1150
Laminated Composite Design......Page 1151
Failure Criteria......Page 1152
Coupling, Balance, and Symmetry......Page 1155
General Laminate Design Philosophy......Page 1157
Fatigue Performance......Page 1158
Safe Life/Reliability Method......Page 1161
Fail Safe/Damage Tolerance Method......Page 1166
The Wearout Model......Page 1167
Damping Characterization......Page 1169
References......Page 1174
Material Damping......Page 1175
Significance of Mechanical Damping as an Engineering Property......Page 1176
Stress-Strain (or Load-Deflection) Hysteresis Loop......Page 1177
Procedures Employing a Vibrating Specimen......Page 1178
Lateral Deflection of Rotating Cantilever Method......Page 1179
Fundamental Relationships......Page 1180
Relationship Between Specific Damping Energy and Stress Level......Page 1181
Volume-Stress Function......Page 1182
Ratio of Damping Energy to Strain Energy......Page 1183
Damping Properties of Materials......Page 1190
Dynamic Hysteresis of Viscoelastic Materials......Page 1193
Static Hysteresis......Page 1195
Comparison of Various Material Damping Mechanisms and Representative Data for Engineering Materials......Page 1197
Damping by Sliding......Page 1199
References......Page 1203
Introduction to the Role of Damping Materials......Page 1205
Polymeric and Elastomeric Materials......Page 1206
Analytical Modeling of Complex Modulus Behavior......Page 1208
Benefits of Applied Damping Treatments......Page 1209
Free-Layer Damping Treatments......Page 1210
Constrained-Layer Damping Treatments......Page 1212
Measures or Criteria of Damping......Page 1215
Comparison of Damping Measures......Page 1221
Methods for Measuring Complex Modulus Properties......Page 1222
References......Page 1226
Introduction......Page 1227
Modeling......Page 1228
Calculation of Polar Moments of Inertia......Page 1229
Calculation of Stiffness......Page 1231
Geared and Branched Systems......Page 1234
Natural Frequency Calculations......Page 1235
Transfer Matrix Method......Page 1236
Finite Element Method......Page 1237
Critical Speeds......Page 1240
General Excitation......Page 1241
Engine Excitation......Page 1242
Exact Method for Two Degree-of-Freedom Systems......Page 1243
Energy Balance Method......Page 1244
Application of Modal Analysis to Rotor Systems......Page 1247
Permissible Amplitudes......Page 1248
American Petroleum Institute......Page 1249
Data Acquisition......Page 1250
Shifting of Critical Speeds......Page 1251
Vector Cancellation Methods......Page 1252
Dampers......Page 1254
References......Page 1259
Basic Principles of Balancing......Page 1260
Rigid-Rotor Balancing - Static Unbalance......Page 1261
Rigid-Rotor Balancing - Dynamic Unbalance......Page 1262
Flexible-Rotor Balancing......Page 1263
Sources of Unbalance......Page 1269
Motions of Unbalanced Rotors......Page 1270
Operating Principles of Balancing Machines......Page 1271
Gravity Balancers......Page 1272
Centrifugal Balancing Machines......Page 1274
Classification of Centrifugal Balancing Machines......Page 1281
Unbalance Correction by the Addition of Weight to the Rotor......Page 1283
Unbalance Correction by the Removal of Weight......Page 1284
Maintenance and Production Balancing Machines......Page 1285
Field Balancing Equipment......Page 1286
Support of the Rotor......Page 1287
Drive for Rotor......Page 1288
Balance Criteria......Page 1289
Definitions......Page 1291
References......Page 1293
Introduction......Page 1295
Use of Spectrum Analysis in Studying Shaft Misalignment......Page 1296
Basic Steps in Shaft Alignment......Page 1297
Reference......Page 1299
Vibration Due to Inhomogeneities in the Workpiece......Page 1300
Disturbances in the Workpiece and Tool Drives......Page 1301
Impacts from Massive Part Reversals......Page 1306
Machine-Tool Chatter......Page 1307
Dynamic Stability......Page 1308
Stiffness......Page 1310
Damping......Page 1317
References......Page 1321
Environments and Requirements......Page 1322
Dynamic Environments......Page 1324
Other Environments......Page 1325
Life-Cycle Analysis......Page 1326
Dynamic Response Constraints and Failure Criteria......Page 1327
Structural Requirements......Page 1328
Other Requirements......Page 1329
Primary Structure......Page 1330
Interfaces and Joints......Page 1332
Subassemblies......Page 1334
Design Criteria......Page 1335
Design Excitation Magnitude......Page 1336
Design Life......Page 1337
Modeling......Page 1338
Preliminary Design Procedures......Page 1341
Final Design Procedures......Page 1344
Design Reviews......Page 1345
Model-Test Correlation......Page 1346
Reliability Growth Testing......Page 1348
References......Page 1349
Introduction......Page 1350
Methods and Instrumentation......Page 1351
Physical Measurements......Page 1352
Simulation of Human Subjects......Page 1353
Physical Data......Page 1355
Low-Frequency Range......Page 1357
Middle-Frequency Range (Wave Propagation)......Page 1366
High-Frequency Range......Page 1368
Effects of Mechanical Vibration......Page 1369
Effects of Mechanical Shock......Page 1372
Effects of Shock and Vibration on Task Performance......Page 1379
Protection Against Vibrations......Page 1380
Protection Against Rapidly Applied Accelerations (Crash)......Page 1383
Whole-Body Vibration Exposure......Page 1389
Acceptability of Building Vibration......Page 1395
Motion Sickness......Page 1397
Hand-Transmitted Vibration......Page 1398
Shock, Impact, and Rapid Deceleration......Page 1400
Biodynamics, Models, and Anthropometric Dummies......Page 1409
Protection Methods and Devices......Page 1410
Tolerance Criteria......Page 1411
Index......Page 1412