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 

Vibration, or oscillation, is a periodic movement in time of a system around a certain equilibrium position. The system consists of at least an element for storing kinetic energy and one for storing potential energy. The vibration is a process of energy-type exchanges between the kinetic and potential energies. The equilibrium position is the state in which the potential energy becomes zero. The periodicity of the movement is described in frequency which is the measurement of the numbers of times the repeated events that occurred in a unit time. Vibration is an omnipresent type of

dynamic behavior of a system and exists in many forms, such as sound and music.

Human beings first recognized the vibration phenomenon by entertaining them?selves with percussion, string, and plate music instruments in ancient times. Just like the time when the lever principle was discovered is much later than that of its real utilization in human history, the time when the vibration and acoustics theory on the principles of the music instruments were discovered is much later than that of the music instruments were made and played. The earliest music instrument unearthed in Henan Province, China, is a bone flute, which can be traced back about 6000–5000 years B.C., while the earliest string vibration frequency and music acoustic theory for a string instrument ever written and published in Chinese history is around 700

B.C. in “Guanzi” by Guan Zhong (723–645 B.C.). In his music-scale algorithm, if the length of the basic string for the major tone is 1, the string lengths of the next scales are either added 1/3 (4/3) of the basic length or subtracted 1/3 (or 2/3), other music scales are determined by this 1/3 length rule, and he obtained five tones by this algorithm:

C, D, E, G, A. It’s amazing that more than 100 years later the Greek Philosopher and Mathematician Pythagoras (570–504 B.C.) discovered independently the very similar theory for seven tones: The Pythagorean scale.

Human beings first learned the vibration and acoustics of the plates and shells also from music instrument manufacturers. “Kaogongji” or “Artificer’s Record” 500 B.C. in Chinese history, recorded the Bian-Qing (sound bian-ching). It is a set of percussion, made of high-quality stones such as jade, with several fixed music scales.

The “Kaogongji” specifically described how to adjust the percussion music scale: “if music scale is higher, filing the surfaces of the plate, if the scale is lower, then filing the edges of the plate”. These technological processes, even though not giving exactly the quantitative relation between the natural frequencies of the plate and its geometrical parameters, are indeed in accordance qualitatively with the contemporary vibration and acoustic principles of the plate and shells: filing the surfaces of the plate makes the plate thinner and natural frequencies will be decreased while filing the edges of the plate makes the plate relatively thicker thus the natural frequencies will be increased.

One of the most important dynamic properties for the vibrations of a system is the inherit frequency or natural frequency. The vibrating movements of a system occur by external forces or internal self-excitement. When the frequencies of the excitation are the same or near the system’s natural frequencies, the responses of the systems will become larger and larger, which is called the resonance. The resonance has a variety of applications, such as radio, television, and music. The large-magnitude vibrations, such as large magnitude earthquakes, tsunamis, could bring harmful,devastative, and even catastrophic damages to properties and human lives. People tried to predict the earthquake by vibrating devices. In 132 A.D. Zhang Heng (78–

139 A.D.), a Chinese mathematician, an astronomer, and a geographer, invented the vibration utilization device: Seismographer. The shape of the device looks like a goblet. Eight (8) exquisitely casting dragons, upside down, attached to the body ofthe device. The eight dragons are mounted in the North, South, East, West, North?east, Southeast, Northwest, and Southwest directions, respectively, representing the earthquake directions. There is a ball in each dragon’s month. There is a vivid toad,mounted separately to the body, under each dragon. It is said that when an earth?quake occurs the dragon in the earthquake direction will release its ball in its mouth into the toad mouth as a prediction indication. The exact mechanism inside was not

well documented. It was recorded in history books that this device had successfully predicted an earthquake about 600 miles away in 138 A.D. just 1 year before he died.

In modern days, tens of thousands of types of vibrating machines and instruments have been successfully used to accomplish a variety of technological procedures in the fields