1 Formation and Development of Vibration Utilization
Engineering ................................................... 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Vibrating Machines and Instruments and Application of Its
Related Technology and Development . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Applications and Developments of Nonlinear Vibration
Utilization Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Applications and Developments of Wave Motion and Wave
Energy Utilization Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 Applications of Electrics, Magnetic and Light Oscillators
in Engineering Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6 Applications of Electrics, Magnetic and Light Oscillators
in Engineering Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.7 Vibrating Phenomena, Patterns and Utilization in Natures . . . . . . . 18
1.8 Vibrating Phenomena, Patterns and Utilization in Human
Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.9 Vista . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Some Important Results in Vibration and Wave Utilization
Engineering Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1 Utilization of Vibrating Conveyors Technology . . . . . . . . . . . . . . . . 22
2.2 Applications of Vibrating Screening Technology . . . . . . . . . . . . . . . 24
2.3 Applications of Vibrating Centrifugal Hydro-Extraction
and Screening Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 Applications of Vibrating Crush and Milling Technology . . . . . . . . 29
2.5 Applications of Vibrating Rolling and Forming Technology . . . . . 31
2.6 Applications of Vibrating Tamping Technology . . . . . . . . . . . . . . . . 33
2.7 Applications of Vibrating Ramming Technology . . . . . . . . . . . . . . . 34
2.8 Applications of Vibration Diagnostics Technology . . . . . . . . . . . . . 35
2.9 Applications of Synchronous Vibrating Theory . . . . . . . . . . . . . . . . 37
2.10 Applications of Resonance Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.10.1 The General Utilization of the Resonance . . . . . . . . . . . . . 38
2.10.2 Application of the Nuclear Magnetic Resonance . . . . . . . . 39
2.11 Applications of Hysteresis System . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.12 Applications of Impact Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.13 Applications of Slow-Changing Parameter Systems . . . . . . . . . . . . 42
2.14 Applications of Chaos Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.15 Applications of Piecewise Inertial Force . . . . . . . . . . . . . . . . . . . . . . 44
2.16 Applications of Piecewise Restoring Force . . . . . . . . . . . . . . . . . . . . 45
2.17 Utilization of Water Wave and Wind Wave . . . . . . . . . . . . . . . . . . . . 46
2.18 Applications of Tense or Elastic Waves . . . . . . . . . . . . . . . . . . . . . . . 47
2.19 Utilization of Supersonic Theory and Technology . . . . . . . . . . . . . . 47
2.19.1 The Application of the Supersonic Motor . . . . . . . . . . . . . . 48
2.19.2 Significance and Function in Medical Diagnostics
of B-Ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.20 Applications of Optical Fiber and Laser Technology . . . . . . . . . . . . 49
2.20.1 Application of the Optical Fiber Technology . . . . . . . . . . . 49
2.20.2 Application of Laser Technology . . . . . . . . . . . . . . . . . . . . . 50
2.21 Utilizations of Ray Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.22 Utilization of Oscillation Theory and Technology . . . . . . . . . . . . . . 51
2.23 Utilization of Vibrating Phenomena and Patterns
in Meteorology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.24 Utilization of Vibrating Phenomena and Patterns in Social
Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.25 Utilizations of Vibrating Principles in Biology Engineering
and Medical Equipments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3 Theory of Vibration Utilization Technology and Equipment
Technological Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.1 Theory and Technological Parameter Computation
of Material Movement on Line Vibration Machine . . . . . . . . . . . . . 57
3.1.1 Theory of Sliding Movement of Materials . . . . . . . . . . . . . 58
3.1.2 Theory of Material Throwing Movement . . . . . . . . . . . . . . 69
3.1.3 Selections of Material Movement State
and Kinematics Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.1.4 Calculation of Real Conveying Speed
and Productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.1.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.2 Theory and Technological Parameter Computation
of Circular and Ellipse Vibration Machine . . . . . . . . . . . . . . . . . . . . 89
3.2.1 Displacement, Velocity and Acceleration
of Vibrating Bed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.2.2 Theory of Material Sliding Movements . . . . . . . . . . . . . . . 91
3.2.3 Theory of Material Throwing Movements . . . . . . . . . . . . . 96
Contents xiii
3.3 Basic Characteristics of Material Movement
in Non-harmonic Vibration Machines . . . . . . . . . . . . . . . . . . . . . . . . 102
3.3.1 Initial Conditions for Positive and Negative Sliding
Movements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.3.2 Stopping Conditions for Positive and Negative
Sliding Movements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.3.3 Calculations of Averaged Material Velocity . . . . . . . . . . . . 104
3.4 Theory on Material Movement in Vibrating Centrifugal
Hydroextractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.4.1 Basic Characteristics of Material Movement
on Upright Vibration Hydroextractor . . . . . . . . . . . . . . . . . 106
3.4.2 Characteristics of Material Movement
on Horizontal Vibration Hydroextractor . . . . . . . . . . . . . . . 114
3.4.3 Computation of Kinematics and Technological
Parameters of Vibration Centrifugal Hydroextractor . . . . . 115
3.5 Probability Theory on Material Screening Process . . . . . . . . . . . . . . 119
3.5.1 Probability of Screening for Material Particle Per
Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.5.2 Falling Incline Angle and Number of Jumps
of Materials on Screen Length . . . . . . . . . . . . . . . . . . . . . . . 123
3.5.3 Calculation of Probability of Material Going
Through Screens for a General Vibration Screen . . . . . . . . 124
3.5.4 Calculation of Probability of Material Going
Through Screens for a Multi-screen Vibrating
Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
3.6 Classification of Screening Method and Probability
Thick-Layer Screening Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
3.6.1 Screening Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
3.6.2 Screening Methods for Probability Thick Layer
Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
3.7 Dynamic Theory of Vibrating Machine Technological
Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4 Linear and Pseudo Linear Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.1 Dynamics of Non-resonant Vibrating Machines of Planer
Single-Axis Inertial Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.2 Dynamics of Non-resonant Vibrating Machines of Spatial
Single-Axis Inertial Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.3 Dynamics of Non-resonant Vibration Machines
of Double-Axis Inertial Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.3.1 Dynamics of Non-resonant Vibrating Machines
of Planer Double-Axis Inertial Type . . . . . . . . . . . . . . . . . . 153
4.3.2 Dynamics of Non-resonant Vibration Machines
of Spatial Double-Axis Inertial Type . . . . . . . . . . . . . . . . . . 157
xiv Contents
4.4 Dynamics of Non-resonant Vibration Machines of Multi-axis
Inertial Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4.4.1 General Pattern of Planer Movement . . . . . . . . . . . . . . . . . . 159
4.4.2 Values of Displacement, Velocity and Acceleration
Curves and Differential Coefficients When θ2 is
Equal to /2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
4.5 Dynamics of Inertial Near-Resonant Type of Vibration
Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
4.5.1 Dynamics of Single Body Near-Resonant Vibration
Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
4.5.2 Dynamics of Double Body Near-Resonant
Vibration Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
4.6 Dynamics of Single Body Elastic Connecting Rod Type
of Near Resonance Vibration Machines . . . . . . . . . . . . . . . . . . . . . . . 168
4.7 Dynamics of Double Body Elastic Connecting Rod Type
of Near Resonance Vibration Machines . . . . . . . . . . . . . . . . . . . . . . . 171
4.7.1 Balanced Type of Vibration Machines with Double
Body Elastically Connecting Rod . . . . . . . . . . . . . . . . . . . . 171
4.7.2 Non-balance Double Body Type of Elastically
Connecting Rod Vibration Machines . . . . . . . . . . . . . . . . . . 173
4.8 Multi-body Elastic-Connecting Rod Type of Near-Resonant
Vibration Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
4.9 Dynamics of Electric–Magnetic Resonant Type of Vibrating
Machines with Harmonic Electric–Magnetic Force . . . . . . . . . . . . . 180
4.9.1 Basic Categories of Electric–Magnetic Forces
of Electric–Magnetic Vibration Machines . . . . . . . . . . . . . 180
4.9.2 Dynamics of Electric–Magnetic Type of Vibrating
Machines with Harmonic Electric–Magnetic Force . . . . . 180
4.9.3 Amplitudes and Phase Angle Differentials
of One-Half-Period Rectification EMTVM . . . . . . . . . . . . 184
4.9.4 Amplitudes and Phase Angle Differentials
of One-Half-Period Plus One-Period Rectification
EMTVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
4.10 Dynamics of Electric–Magnetic Type of Near-Resonant
Vibration Machines with Non-Harmonic Electric–Magnetic
Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
4.10.1 Relationships Between Electric–Magnetic Force
and Amplitudes of Controlled One-Half-Period
Rectification EMTVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
4.10.2 Relationships Between Electric–Magnetic Force
and Amplitudes of the Decreased Frequency
EMTVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Contents xv
5 Utilization of Nonlinear Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
5.2 Utilization of Smooth Nonlinear Vibration Systems . . . . . . . . . . . . 201
5.2.1 Measurement of Dry Friction Coefficients Between
Axis and Its Bushing Using Double Pendulum . . . . . . . . . 201
5.2.2 Measurement of Dynamic Friction Coefficients
of Rolling Bearing Using Flode Pendulum . . . . . . . . . . . . . 203
5.2.3 Increase the Stability of Vibrating Machines Using
Hard-Smooth Nonlinear Vibrating Systems . . . . . . . . . . . . 207
5.3 Engineering Utilization of Piece-Wise-Linear Nonlinear
Vibration Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
5.3.1 Hard-Symmetric Piece-Wise Linear Vibration
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
5.3.2 Soft-Asymmetric Piece-Wise Linear Vibration
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
5.3.3 Nonlinear Vibration Systems with Complex
Piece-Wise Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
5.4 Utilization of Vibration Systems with Hysteresis Nonlinear
Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
5.4.1 Simplest Hysteresis Systems . . . . . . . . . . . . . . . . . . . . . . . . 223
5.4.2 Hysteresis Systems with Gaps . . . . . . . . . . . . . . . . . . . . . . . 226
5.5 Utilization of Self-excited Vibration Systems . . . . . . . . . . . . . . . . . . 231
5.6 Utilization of Nonlinear Vibration Systems with Impact . . . . . . . . . 233
5.7 Utilization of Frequency-Entrainment Principles . . . . . . . . . . . . . . . 236
5.7.1 Synchronous Theory of Self-synchronous Vibrating
Machine with Eccentric Exciter . . . . . . . . . . . . . . . . . . . . . . 238
5.7.2 Double Frequency Synchronization of Nonlinear
Self-synchronous Vibration Machines . . . . . . . . . . . . . . . . . 250
5.8 Utilization of Nonlinear Vibration Systems with Nonlinear
Inertial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
5.8.1 Movement Equations for Vibration Centrifugal
Hydro-Extractor with Nonlinear Inertial Force . . . . . . . . . 259
5.8.2 Nonlinear Vibration Responses of Vibration
Centrifugal Hydro-Extractor . . . . . . . . . . . . . . . . . . . . . . . . . 261
5.8.3 Frequency-Magnitude Characteristics of Vibration
Centrifugal Hydro-Extractor . . . . . . . . . . . . . . . . . . . . . . . . . 263
5.8.4 Experiment Vibration Responses of Vibration
Centrifugal Hydro-Extractor . . . . . . . . . . . . . . . . . . . . . . . . . 264
5.9 Utilization of Slowly-Changing Parameter Nonlinear
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
5.9.1 Slowly-Changing Systems Formed in Processes
of Starting and Stopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
5.9.2 Slowly-Changing Rotor Systems Formed in Active
Control Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
xvi Contents
5.10 Utilization of Chaos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
5.10.1 Major Methods for Studying Chaos . . . . . . . . . . . . . . . . . . . 271
5.10.2 Software of Studying Chaos Problems . . . . . . . . . . . . . . . . 273
5.10.3 Application Examples of Chaos . . . . . . . . . . . . . . . . . . . . . . 275
6 Utilization of Wave and Wave Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
6.1 Utilization of Tidal Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
6.2 Utilization of Sea Wave Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
6.3 Utilization of Stress Wave in Vibrating Oil Exploration . . . . . . . . . 288
6.3.1 Mechanism and Working Principles of Controllable
Super-Low Frequency Vibration Exciters . . . . . . . . . . . . . . 289
6.3.2 Effect of Stress Wave on Oil Layers . . . . . . . . . . . . . . . . . . 290
6.3.3 Experiment Results and Analysis . . . . . . . . . . . . . . . . . . . . . 299
6.3.4 Elastic Stress Wave Propagation When
a Controllable Vibration Source is Working . . . . . . . . . . . . 305
7 Utilization of Vibrating Phenomena and Patterns in Nature
and Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
7.1 Utilization of Vibration Phenomena and Patterns
in Meteorology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
7.2 Periodical Vibration and Utilization of the Tide . . . . . . . . . . . . . . . . 316
7.3 Vibration Patterns and Utilization in Other Natural
Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
7.3.1 Periodical Phenomenon of Tree Year-Rings . . . . . . . . . . . . 318
7.3.2 Bee’s Communications Using Vibrations . . . . . . . . . . . . . . 319
7.4 Utilization of Vibration Phenomena and Patterns in Some
Economy Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
7.4.1 Fluctuation and Nonlinear Characteristics in Social
Economy Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
7.4.2 Growth and Decline Period in Social Economy
Development Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
7.4.3 Active Role of Macro-adjustment in Preventing
Big Economy Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . 325
7.5 Utilization of Vibration Phenomena and Patterns in Stock
Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
7.5.1 Stock Fluctuation is One of Typical Types
of Economy Change Form in Social Economy Fields . . . . 326
7.5.2 Stock Market Characteristics and General Patterns
of Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
7.5.3 Some Principles in Stock Operations . . . . . . . . . . . . . . . . . . 332
7.6 Obey the General Rules in the Stock Operations . . . . . . . . . . . . . . . 332
7.7 The Entering Point and Withdrawing Points in the Stock
Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
Contents xvii
7.8 Utilization of Vibration Phenomena and Pattern in Human
Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
7.8.1 Vibration is a Basic Existing Form of Many Human
Organs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
7.8.2 Some Diseases Make Abnormal Fluctuations
(Vibration) in Human Organs Physical Parameters . . . . . . 336
7.8.3 Medical Devices and Equipment Based
on Vibration Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
7.8.4 Artificial Organs and Devices Using Vibration
Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
7.9 Prospect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
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