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Shock and Vibration Handbook

Engineering and Design for Vibration

Shock and Vibration Handbook
Pages 1768
Clarence W. De Silva
Editor in Chief

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Preface

In this handbook, equal emphasis is given to theory and practical application. The chapters are grouped into fundamentals, basic theory, advanced theory, analytical techniques, numerical techniques, experimental techniques, design methodology, practical problems and solutions, applications, regulatory considerations, and useful data. Analytical formulations, numerical methods, design approaches, control techniques, and commercial software tools are presented and illustrated. Commercial equipment, computer hardware, and instrumentation are described, analyzed, and demonstrated for field application, practical implementation, and experimentation. Examples and case studies are given throughout the handbook to illustrate the use and application of the included information. The material is presented in a format that is convenient for easy reference and recollection.

Mechanical vibration is a manifestation of oscillatory behavior in mechanical systems, as a result of either the repetitive interchange of kinetic and potential energies among components in the system, or a forcing excitation that is oscillatory. Such oscillatory responses are not limited to purely mechanical systems, and are found in electrical and fluid systems as well. In purely thermal systems, however, free natural oscillations are not possible, and an oscillatory excitation is needed to obtain an oscillatory response. Shock is vibration caused by brief, abrupt, and typically high-intensity excitations. Sound, noise, and acoustics are manifestations of pressure waves, sources of which are often vibratory dynamic systems.

Low levels of vibration mean reduced noise and an improved work environment. Vibration modification and control can be crucial in maintaining high performance and production efficiency, and prolonging the useful life in industrial machinery. Consequently, a considerable effort is devoted today to studying and controlling the vibration and shock generated by machinery components, machine tools, transit vehicles, impact processes, civil engineering structures, fluid flow systems, and aircraft. Noise and acoustic problems can originate from undesirable vibrations and fluid – structure interactions, as found, for example, in automobile engines. Engine noise, environmental noise, and noise from high-speed and high-temperature exhaust gases in a vehicle will not only cause passenger discomfort and public annoyance, they will also result in damaging effects to the vehicle itself. Noise-suppression methods and devices, and sound-absorption material and structures are crucial in such situations. Before designing or controlling a system for good vibratory or acoustic performance, it is important to understand, analyze, and represent the dynamic characteristics of the system. This may be accomplished through purely analytical means, computer analysis of analytical models, testing and analysis of test data, or by a combination of these approaches. It follows that modeling, analysis, testing, and design are all important aspects of study in vibration, shock, and acoustics.

TOC

SECTION I Fundamentals and Analysis
1 Time-Domain Analysis Clarence W. de Silva 1-1
1.1 Introduction . 1-1
1.2 Undamped Oscillator .. 1-2
1.3 Heavy Springs 1-12
1.4 Oscillations in Fluid Systems .. 1-14
1.5 Damped Simple Oscillator 1-16
1.6 Forced Response .. 1-27
2 Frequency-Domain Analysis Clarence W. de Silva .. 2-1
2.1 Introduction . 2-1
2.2 Response to Harmonic Excitations . 2-2
2.3 Transform Techniques .. 2-14
2.4 Mechanical Impedance Approach . 2-25
2.5 Transmissibility Functions . 2-31
2.6 Receptance Method 2-37
Appendix 2A Transform Techniques .. 2-40
3 Modal Analysis Clarence W. de Silva . 3-1
3.1 Introduction . 3-1
3.2 Degrees of Freedom and Independent Coordinates 3-2
3.3 System Representation 3-4
3.4 Modal Vibrations 3-10
3.5 Orthogonality of Natural Modes .. 3-14
3.6 Static Modes and Rigid-Body Modes . 3-15
3.7 Other Modal Formulations .. 3-22
3.8 Forced Vibration . 3-28
3.9 Damped Systems . 3-32
3.10 State-Space Approach .. 3-36
Appendix 3A Linear Algebra 3-41
4 Distributed-Parameter Systems Clarence W. de Silva 4-1
4.1 Introduction . 4-1
4.2 Transverse Vibration of Cables . 4-2
4.3 Longitudinal Vibrations of Rods .. 4-13
4.4 Torsional Vibration of Shafts .. 4-19
4.5 Flexural Vibration of Beams . 4-26
4.6 Damped Continuous Systems . 4-50
4.7 Vibration of Membranes and Plates 4-52
5 Random Vibration Haym Benaroya . 5-1
5.1 Random Vibration 5-1
5.2 Single Degree of Freedom: The Response to Random Loads 5-2
5.3 Response to Two Random Loads . 5-7
5.4 Multi-Degree-of-Freedom Vibration .. 5-12
5.5 Multi-Degree-of-Freedom: The Response to Random Loads . 5-17
5.6 Continuous System Random Vibration 5-29

SECTION II Computer Techniques
6 Numerical Techniques Marie D. Dahleh .. 6-1
6.1 Introduction . 6-1
6.2 Single-Degree-of-Freedom System .. 6-2
6.3 Systems with Two or More Degrees of Freedom 6-8
6.4 Finite Difference Method for a Continuous System . 6-11
6.5 Matrix Methods 6-14
6.6 Approximation Methods for the Fundamental Frequency 6-18
6.7 Finite Element Method 6-20
7 Vibration Modeling and Software Tools Datong Song, Cheng Huang, and Zhong-Sheng Liu .. 7-1
7.1 Introduction . 7-1
7.2 Formulation . 7-2
7.3 Vibration Analysis . 7-9
7.4 Commercial Software Packages .. 7-13
7.5 The Basic Procedure of Vibration Analysis . 7-16
7.6 An Engineering Case Study .. 7-19
7.7 Comments .. 7-21
8 Computer Analysis of Flexibly Supported Multibody Systems Ibrahim Esat and M. Dabestani 8-1
8.1 Introduction . 8-1
8.2 Theory . 8-2
8.3 A Numerical Example . 8-7
8.4 An Industrial Vibration Design Problem . 8-11
8.5 Programming Considerations . 8-16
8.6 VIBRATIO .. 8-17
8.7 Analysis . 8-24
8.8 Comments .. 8-31
Appendix 8A VIBRATIO Output for Numerical Example in Section 8.3 .. 8-32
9 Finite Element Applications in Dynamics Mohamed S. Gadala 9-1
9.1 Problem and Element Classification .. 9-2
9.2 Types of Analysis . 9-20
9.3 Modeling Aspects for Dynamic Analysis .. 9-23
9.4 Equations of Motion and Solution Methods . 9-27
9.5 Various Dynamic Analyses 9-33
9.6 Checklist for Dynamic FE Analysis . 9-41
10 Vibration Signal Analysis Clarence W. de Silva 10-1
10.1 Introduction 10-1
10.2 Frequency Spectrum .. 10-2
10.3 Signal Types 10-7
10.4 Fourier Analysis 10-7
10.5 Analysis of Random Signals .. 10-18
10.6 Other Topics of Signal Analysis .. 10-26
10.7 Overlapped Processing .. 10-28
11 Wavelets — Concepts and Applications Pol D. Spanos, Giuseppe Failla, and Nikolaos P. Politis . 11-1
11.1 Introduction 11-1
11.2 Time – Frequency Analysis . 11-2
11.3 Time-Dependent Spectra Estimation of Stochastic Processes .. 11-11
11.4 Random Field Simulation .. 11-14
11.5 System Identification .. 11-15
11.6 Damage Detection 11-17
11.7 Material Characterization 11-18
11.8 Concluding Remarks .. 11-19

SECTION III Shock and Vibration
12 Mechanical Shock Christian Lalanne 12-1
12.1 Definitions . 12-2
12.2 Description in the Time Domain . 12-3
12.3 Shock Response Spectrum . 12-4
12.4 Pyroshocks 12-17
12.5 Use of Shock Response Spectra 12-18
12.6 Standards .. 12-24
12.7 Damage Boundary Curve 12-26
12.8 Shock Machines . 12-28
12.9 Generation of Shock Using Shakers . 12-44
12.10 Control by a Shock Response Spectrum 12-52
12.11 Pyrotechnic Shock Simulation . 12-58
13 Vibration and Shock Problems of Civil Engineering Structures Priyan Mendis and Tuan Ngo .. 13-1
13.1 Introduction 13-2
13.2 Earthquake-Induced Vibration of Structures 13-3
13.3 Dynamic Effects of Wind Loading on Structures . 13-22 13.4
Vibrations Due to Fluid – Structure Interaction 13-33 13.5
Blast Loading and Blast Effects on Structures 13-34 13.6
Impact Loading . 13-47 13.7
Floor Vibration .. 13-51 14
Reinforced Concrete Structures Y.L. Mo 14-1 14.1
Introduction 14-1 14.2
Analytical Models 14-6 14.3
Beams under Harmonic Excitations . 14-18 14.4
Design for Explosions/Shocks .. 14-21

SECTION IV Instrumentation and Testing
15 Vibration Instrumentation Clarence W. de Silva 15-1
15.1 Introduction 15-1
15.2 Vibration Exciters 15-3
15.3 Control System .. 15-15
15.4 Performance Specification .. 15-21
15.5 Motion Sensors and Transducers 15-27
15.6 Torque, Force, and Other Sensors . 15-50
Appendix 15A Virtual Instrumentation for Data Acquisition, Analysis, and Presentation 15-73
16 Signal Conditioning and Modification Clarence W. de Silva . 16-1
16.1 Introduction 16-2
16.2 Amplifiers 16-2
16.3 Analog Filters .. 16-15
16.4 Modulators and Demodulators 16-29
16.5 Analog – Digital Conversion 16-37
16.6 Bridge Circuits 16-43
16.7 Linearizing Devices . 16-49
16.8 Miscellaneous Signal Modification Circuitry .. 16-56
16.9 Signal Analyzers and Display Devices . 16-62
17 Vibration Testing Clarence W. de Silva . 17-1
17.1 Introduction 17-1
17.2 Representation of a Vibration Environment .. 17-3
17.3 Pretest Procedures 17-24
17.4 Testing Procedures 17-37
17.5 Some Practical Information .. 17-52
18 Experimental Model Analysis Clarence W. de Silva . 18-1
18.1 Introduction 18-1
18.2 Frequency-Domain Formulation .. 18-2
18.3 Experimental Model Development .. 18-8
18.4 Curve Fitting of Transfer Functions . 18-10
18.5 Laboratory Experiments .. 18-18
18.6 Commercial EMA Systems . 18-24

SECTION V Vibration Suppression and Control
19 Vibration Damping Clarence W. de Silva .. 19-1
19.1 Introduction 19-1
19.2 Types of Damping .. 19-2
19.3 Representation of Damping in Vibration Analysis 19-9
19.4 Measurement of Damping .. 19-16
19.5 Interface Damping 19-26
20 Damping Theory Randall D. Peters 20-1
20.1 Preface .. 20-2
20.2 Introduction 20-4
20.3 Background .. 20-12
20.4 Hysteresis — More Details . 20-19
20.5 Damping Models .. 20-20
20.6 Measurements of Damping 20-23
20.7 Hysteretic Damping 20-27
20.8 Failure of the Common Theory .. 20-29
20.9 Air Influence 20-30
20.10 Noise and Damping 20-31
20.11 Transform Methods . 20-34
20.12 Hysteretic Damping 20-36
20.13 Internal Friction 20-41
20.14 Mathematical Tricks — Linear Damping Approximations 20-43
20.15 Internal Friction Physics .. 20-44
20.16 Zener Model 20-45
20.17 Toward a Universal Model of Damping . 20-48
20.18 Nonlinearity . 20-58
20.19 Concluding Remark 20-65
21 Experimental Techniques in Damping Randall D. Peters . 21-1
21.1 Electronic Considerations .. 21-2
21.2 Data Processing 21-3
21.3 Sensor Choices .. 21-7
21.4 Damping Examples 21-8
21.5 Driven Oscillators with Damping .. 21-19
21.6 Oscillator with Multiple Nonlinearities . 21-21
21.7 Multiple Modes of Vibration 21-24
21.8 Internal Friction as Source of Mechanical Noise . 21-28
21.9 Viscous Damping — Need for Caution . 21-29
21.10 Air Influence 21-31
22 Structure and Equipment Isolation Y.B. Yang, L.Y. Lu, and J.D. Yau . 22-1
22.1 Introduction 22-2
22.2 Mechanisms of Base-Isolated Systems 22-4
22.3 Structure – Equipment Systems with Elastomeric Bearings .. 22-9
22.4 Sliding Isolation Systems . 22-17
22.5 Sliding Isolation Systems with Resilient Mechanism . 22-36
22.6 Issues Related to Seismic Isolation Design .. 22-50
23 Vibration Control Nader Jalili and Ebrahim Esmailzadeh 23-1
23.1 Introduction 23-1
23.2 Vibration-Control Systems Concept 23-4
23.3 Vibration-Control Systems Design and Implementation 23-12
23.4 Practical Considerations and Related Topics .. 23-38
24 Helicopter Rotor Tuning Kourosh Danai . 24-1
24.1 Introduction 24-1
24.2 Neural Network-Based Tuning 24-4
24.3 Probability-Based Tuning .. 24-5
24.4 Adaptive Tuning .. 24-8
24.5 Case Study . 24-12
24.6 Conclusion 24-17

SECTION VI Monitoring and Diagnosis
25 Machine Condition Monitoring and Fault Diagnostics Chris K. Mechefske .. 25-1
25.1 Introduction 25-2
25.2 Machinery Failure .. 25-2
25.3 Basic Maintenance Strategies .. 25-4
25.4 Factors which Influence Maintenance Strategy 25-7
25.5 Machine Condition Monitoring 25-8
25.6 Transducer Selection .. 25-10
25.7 Transducer Location 25-14
25.8 Recording and Analysis Instrumentation .. 25-14
25.9 Display Formats and Analysis Tools . 25-16
25.10 Fault Detection .. 25-21
25.11 Fault Diagnostics .. 25-25
26 Vibration-Based Tool Condition Monitoring Systems C. Scheffer and P.S. Heyns .. 26-1
26.1 Introduction 26-1
26.2 Mechanics of Turning .. 26-2
26.3 Vibration Signal Recording .. 26-7
26.4 Signal Processing for Sensor-Based Tool Condition Monitoring .. 26-11
26.5 Wear Model/Decision-Making for Sensor-Based Tool Condition Monitoring . 26-15
26.6 Conclusion 26-20
27 Fault Diagnosis of Helicopter Gearboxes Kourosh Danai 27-1
27.1 Introduction 27-1
27.2 Abnormality Scaling .. 27-5
27.3 The Structure-Based Connectionist Network 27-8
27.4 Sensor Location Selection 27-11
27.5 A Case Study 27-14
27.6 Conclusion 27-23
28 Vibration Suppression and Monitoring in Precision Motion Systems K.K. Tan, T.H. Lee, K.Z. Tang, S. Huang, S.Y. Lim, W. Lin, and Y.P. Leow .. 28-1
28.1 Introduction 28-1
28.2 Mechanical Design to Minimize Vibration . 28-2
28.3 Adaptive Notch Filter . 28-10
28.4 Real-Time Vibration Analyzer .. 28-17
28.5 Practical Insights and Case Study .. 28-29
28.6 Conclusions .. 28-35

SECTION VII Seismic Vibration
29 Seismic Base Isolation and Vibration Control Hirokazu Iemura, Sarvesh Kumar Jain, and Mulyo Harris Pradono .. 29-1
29.1 Introduction 29-1
29.2 Seismic Base Isolation .. 29-4
29.3 Seismic Vibration Control .. 29-33
30 Seismic Random Vibration of Long-Span Structures Jiahao Lin and Yahui Zhang 30-1
30.1 Introduction 30-2
30.2 Seismic Random Excitation Fields . 30-11
30.3 Pseudoexcitation Method for Structural Random Vibration Analysis 30-16
30.4 Long-Span Structures Subjected to Stationary Random Ground Excitations 30-27
30.5 Long-Span Structures Subjected to Nonstationary Random Ground Excitations .. 30-34
30.6 Conclusions .. 30-39
31 Seismic Qualification of Equipment Clarence W. de Silva 31-1
31.1 Introduction 31-1
31.2 Distribution Qualification . 31-1
31.3 Seismic Qualification 31-6

SECTION VIII Design and Applications
32 Vibration Design and Control Clarence W. de Silva .. 32-1
32.1 Introduction 32-2
32.2 Specification of Vibration Limits .. 32-3
32.3 Vibration Isolation . 32-5
32.4 Balancing of Rotating Machinery .. 32-15
32.5 Balancing of Reciprocating Machines . 32-26
32.6 Whirling of Shafts 32-33
32.7 Design through Modal Testing . 32-39
32.8 Passive Control of Vibration . 32-45
32.9 Active Control of Vibration .. 32-61
32.10 Control of Beam Vibrations .. 32-67
Appendix 32A MATLAB Control Systems Toolbox .. 32-73
33 Structural Dynamic Modification and Sensitivity Analysis Su Huan Chen .. 33-1
33.1 Introduction 33-2
33.2 Structural Dynamic Modification of Finite Element Model 33-2
33.3 Perturbation Method of Vibration Modes .. 33-4
33.4 Design Sensitivity Analysis of Structural Vibration Modes . 33-8
33.5 High-Accuracy Modal Superposition for Sensitivity Analysis of Modes .. 33-11
33.6 Sensitivity of Eigenvectors for Free – Free Structures . 33-13
33.7 Matrix Perturbation Theory for Repeated Modes .. 33-14
33.8 Matrix Perturbation Method for Closely Spaced Eigenvalues . 33-16
33.9 Matrix Perturbation Theory for Complex Modes .. 33-22
34 Vibration in Rotating Machinery H. Sam Samarasekera 34-1
34.1 Introduction 34-1
34.2 Vibration Basics 34-6
34.3 Rotordynamic Analysis . 34-18
34.4 Vibration Measurement and Techniques .. 34-39
34.5 Vibration Control and Diagnostics .. 34-39
35 Regenerative Chatter in Machine Tools Robert G. Landers . 35-1
35.1 Introduction 35-1
35.2 Chatter in Turning Operations .. 35-3
35.3 Chatter in Face-Milling Operations . 35-9
35.4 Time-Domain Simulation .. 35-14
35.5 Chatter Detection . 35-18
35.6 Chatter Suppression 35-20
35.7 Case Study . 35-24
36 Fluid-Induced Vibration Seon M. Han . 36-1
36.1 Description of the Ocean Environment 36-1
36.2 Fluid Forces .. 36-16
36.3 Examples .. 36-23

SECTION IX Acoustics
37 Sound Levels and Decibels S. Akishita .. 37-1
37.1 Introduction 37-1
37.2 Sound Wave Characteristics . 37-1
37.3 Levels and Decibels 37-3
38 Hearing and Psychological Effects S. Akishita 38-1
38.1 Introduction 38-1
38.2 Structure and Function of the Ear 38-1
38.3 Frequency and Loudness Response . 38-2
38.4 Hearing Loss .. 38-4
38.5 Psychological Effects of Noise . 38-4
39 Noise Control Criteria and Regulations S. Akishita . 39-1
39.1 Introduction 39-1
39.2 Basic Ideas behind Noise Policy . 39-1
39.3 Legislation .. 39-2
39.4 Regulation .. 39-4
39.5 Measures of Noise Evaluation . 39-5
40 Instrumentation Kiyoshi Nagakura . 40-1
40.1 Sound Intensity Measurement 40-1
40.2 Mirror– Microphone System 40-4
40.3 Microphone Array .. 40-6
41 Source of Noise S. Akishita .. 41-1
41.1 Introduction 41-1
41.2 Radiation of Sound 41-1
42 Design of Absorption Teruo Obata .. 42-1
42.1 Introduction 42-1
42.2 Fundamentals of Sound Absorption .. 42-2
42.3 Sound-Absorbing Materials .. 42-3
42.4 Acoustic Characteristic Computation of Compound Wall .. 42-6
42.5 Attenuation of Lined Ducts 42-10
42.6 Attenuation of Dissipative Mufflers .. 42-12
42.7 General Considerations . 42-15
42.8 Practical Example of Dissipative Muffler .. 42-17
43 Design of Reactive Mufflers Teruo Obata 43-1
43.1 Introduction 43-1
43.2 Fundamental Equations .. 43-2
43.3 Effects of Reactive Mufflers 43-3
43.4 Calculation Procedure .. 43-5
43.5 Application Range of Model 43-6
43.6 Practical Example . 43-13
44 Design of Sound Insulation Kiyoshi Okura 44-1
44.1 Theory of Sound Insulation . 44-1
44.2 Application of Sound Insulation 44-13
45 Statistical Energy Analysis Takayuki Koizumi 45-1
45.1 Introduction 45-1
45.2 Power Flow Equations . 45-2
45.3 Estimation of Sea Parameters .. 45-4
45.4 Application in Structures 45-7

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