ISBN-10:
1848216440
ISBN-13:
9781848216440
Pub. Date:
04/07/2014
Publisher:
Wiley
Mechanical Vibration and Shock Analysis, Sinusoidal Vibration / Edition 3

Mechanical Vibration and Shock Analysis, Sinusoidal Vibration / Edition 3

by Christian Lalanne
Current price is , Original price is $206.95. You

Temporarily Out of Stock Online

Please check back later for updated availability.

This item is available online through Marketplace sellers.

Product Details

ISBN-13: 9781848216440
Publisher: Wiley
Publication date: 04/07/2014
Series: ISTE Series
Edition description: Volume 1
Pages: 1734
Product dimensions: 9.20(w) x 6.10(h) x 1.20(d)

About the Author

Christian Lalanne is a Consultant Engineer who previously worked as an expert at the French Atomic Energy Authority and who has specialized in the study of vibration and shock for more than 40 years. He has been associated with the new methods of drafting testing specifications and associated informatic tools.

Read an Excerpt

Click to read or download

Table of Contents

Foreword to Series xi

Introduction   xv

List of Symbols xix

Chapter 1. The Need 1

1.1. The need to carry out studies into vibrations and mechanical shocks 1

1.2. Some real environments 3

1.2.1. Sea transport 3

1.2.2. Earthquakes 5

1.2.3. Road vibratory environment 6

1.2.4. Rail vibratory environment   7

1.2.5. Propeller airplanes 8

1.2.6. Vibrations caused by jet propulsion airplanes  8

1.2.7. Vibrations caused by turbofan aircraft 9

1.2.8. Helicopters 9

1.3. Measuring vibrations and shocks 11

1.4. Filtering   15

1.4.1. Definitions 15

1.4.2. Digital filters 18

1.5. Digitizing the signal 21

1.5.1. Signal sampling frequency   21

1.5.2. Quantization error 25

1.6. Reconstructing the sampled signal  28

1.7. Characterization in the frequency domain 31

1.8. Elaboration of the specifications 32

1.9. Vibration test facilities 33

1.9.1. Electro-dynamic exciters  33

1.9.2. Hydraulic actuators 37

1.9.3. Test Fixtures 38

Chapter 2. Basic Mechanics  41

2.1. Basic principles of mechanics  41

2.1.1. Principle of causality 41

2.1.2. Concept of force  41

2.1.3. Newton’s first law (inertia principle) 42

2.1.4. Moment of a force around a point 42

2.1.5. Fundamental principle of dynamics (Newton’s second law)   43

2.1.6. Equality of action and reaction (Newton’s third law ) 43

2.2. Static effects/dynamic effects  43

2.3. Behavior under dynamic load (impact) 45

2.4. Elements of a mechanical system 48

2.4.1. Mass 48

2.4.2. Stiffness 49

2.4.3. Damping 57

2.4.4. Static modulus of elasticity   71

2.4.5. Dynamic modulus of elasticity  72

2.5. Mathematical models  74

2.5.1. Mechanical systems 74

2.5.2. Lumped parameter systems   75

2.5.3. Degrees of freedom   77

2.5.4. Mode 77

2.5.5. Linear systems 79

2.5.6. Linear one-degree-of-freedom mechanical systems 79

2.6. Setting an equation for n degrees-of-freedom lumped parameter mechanical system 80

2.6.1. Lagrange equations 80

2.6.2. D’Alembert’s principle88

2.6.3. Free-body diagram 88

Chapter 3. Response of a Linear One-Degree-of-Freedom Mechanical System to an Arbitrary Excitation 97

3.1. Definitions and notation 97

3.2. Excitation defined by force versus time 99

3.3. Excitation defined by acceleration  103

3.4. Reduced form 104

3.4.1. Excitation defined by a force on a mass or by an acceleration of support   104

3.4.2. Excitation defined by velocity or displacement imposed on support 106

3.5. Solution of the differential equation of movement  109

3.5.1. Methods 109

3.5.2. Relative response  109

3.5.3. Absolute response 113

3.5.4. Summary of main results  118

3.6. Natural oscillations of a linear one-degree-of-freedom system  119

3.6.1. Damped aperiodic mode   120

3.6.2. Critical aperiodic mode 124

3.6.3. Damped oscillatory mode  127

Chapter 4. Impulse and Step Responses  145

4.1. Response of a mass–spring system to a unit step function (step or indicial response)  145

4.1.1. Response defined by relative displacement  145

4.1.2. Response defined by absolute displacement, velocity or acceleration 153

4.2. Response of a mass–spring system to a unit impulse excitation  158

4.2.1. Response defined by relative displacement  158

4.2.2. Response defined by absolute parameter 164

4.3. Use of step and impulse responses  169

4.4. Transfer function of a linear one-degree-of-freedom system  176

4.4.1. Definition 176

4.4.2. Calculation of H(h) for relative response   179

4.4.3. Calculation of H(h) for absolute response   180

4.4.4. Other definitions of the transfer function 182

4.5. Measurement of transfer function 188

Chapter 5. Sinusoidal Vibration   189

5.1. Definitions  189

5.1.1. Sinusoidal vibration 189

5.1.2. Mean value 191

5.1.3. Mean square value – rms value 192

5.1.4. Periodic vibrations 195

5.1.5. Quasi-periodic signals   198

5.2. Periodic and sinusoidal vibrations in the real environment 199

5.3. Sinusoidal vibration tests 199

Chapter 6. Response of a Linear One-Degree-of-Freedom Mechanical System to a Sinusoidal Excitation 203

6.1. General equations of motion 204

6.1.1. Relative response  204

6.1.2. Absolute response 207

6.1.3. Summary 209

6.1.4. Discussion 210

6.1.5. Response to periodic excitation 212

6.1.6. Application to calculation for vehicle suspension response  213

6.2. Transient response  215

6.2.1. Relative response  215

6.2.2. Absolute response 219

6.3. Steady state response  219

6.3.1. Relative response  219

6.3.2. Absolute response 220

6.4. Responses |ω o z./x..m|,|ω o z/x.m| and |√kmz./Fm|

6.4.1. Amplitude and phase 221

6.4.2. Variations of velocity amplitude 222

6.4.3. Variations in velocity phase  234

6.5. Responses k2/Fm , ωo²z/x..m

6.5.1. Expression for response 235

6.5.2. Variation in response amplitude 236

6.5.3. Variations in phase 241

6.6. Responses y/xm, .y/.x, ÿ/..xm and FT/Fm

6.6.1. Movement transmissibility   249

6.6.2. Variations in amplitude 250

6.6.3. Variations in phase 253

6.7. Graphical representation of transfer functions   255

6.8. Definitions  257

6.8.1. Compliance – stiffness   257

6.8.2. Mobility – impedance   258

6.8.3. Inertance – mass  259

Chapter 7. Non-viscous Damping 261

7.1. Damping observed in real structures 261

7.2. Linearization of non-linear hysteresis loops – equivalent viscous damping 262

7.3. Main types of damping 266

7.3.1. Damping force proportional to the power b of the relative velocity   266

7.3.2. Constant damping force 267

7.3.3. Damping force proportional to the square of velocity 269

7.3.4. Damping force proportional to the square of displacement  270

7.3.5. Structural or hysteretic damping 271

7.3.6. Combination of several types of damping   272

7.3.7. Validity of simplification by equivalent viscous damping 273

7.4. Measurement of damping of a system 274

7.4.1. Measurement of amplification factor at resonance  274

7.4.2. Bandwidth or √2 method  276

7.4.3. Decreased rate method (logarithmic decrement)  277

7.4.4. Evaluation of energy dissipation under permanent sinusoidal vibration  284

7.4.5. Other methods  288

7.5. Non-linear stiffness 288

Chapter 8. Swept Sine 291

8.1. Definitions  291

8.1.1. Swept sine 291

8.1.2. Octave – number of octaves in frequency interval ƒ1 ƒ2  294

8.1.3. Decade  294

8.2. “Swept sine” vibration in the real environment 295

8.3. “Swept sine” vibration in tests 295

8.4. Origin and properties of main types of sweepings  297

8.4.1. The problem 297

8.4.2. Case 1: sweep where time Δt spent in each interval Δf is constant for all values of f0 301

8.4.3. Case 2: sweep with constant rate313

8.4.4. Case 3: sweep ensuring a number of identical cycles ?´N in all intervals ?´f (delimited by the half-power points) for all values of f0. 314

Chapter 9. Response of a Linear One-Degree-of-Freedom System to a Swept Sine Vibration 319

9.1. Influence of sweep rate 319

9.2. Response of a linear one-degree-of-freedom system to a swept sine excitation 321

9.2.1. Methods used for obtaining response 321

9.2.2. Convolution integral (or Duhamel’s integral)  322

9.2.3. Response of a linear one-degree-of freedom system to a linear swept sine excitation 324

9.2.4. Response of a linear one-degree-of-freedom system to a logarithmic swept sine 334

9.3. Choice of duration of swept sine test 338

9.4. Choice of amplitude 342

9.5. Choice of sweep mode 343

Appendix. Laplace Transformations   353

Vibration Tests: a Brief Historical Background 367

Bibliography  373

Index  387

Summary of Other Volumes in the Series 393

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews