Mechanical Vibration and Shock Analysis, Specification Development (3^rd Ed., Volume 5)
Specification Development
Mechanical Vibration and Shock Analysis Series

Everything engineers need to know about mechanical vibration and shock...in one authoritative reference work!

This fully updated and revised 3rd edition addresses the entire field of mechanical vibration and shock as one of the most important types of load and stress applied to structures, machines and components in the real world. Examples include everything from the regular and predictable loads applied to turbines, motors or helicopters by the spinning of their constituent parts to the ability of buildings to withstand damage from wind loads or explosions, and the need for cars to maintain structural integrity in the event of a crash. There are detailed examinations of underlying theory, models developed for specific applications, performance of materials under test conditions and in real-world settings, and case studies and discussions of how the relationships between these affect design for actual products.

Invaluable to engineers specializing in mechanical, aeronautical, civil, electrical and transportation engineering, this reference work, in five volumes is a crucial resource for the solution of shock and vibration problems.

This volume focuses on specification development in accordance with the principle of tailoring. Extreme response and the fatigue damage spectra are defined for each type of stress (sinusoidal vibration, swept sine, shock, random vibration, etc.). The process for establishing a specification from the life cycle profile of equipment which will be subject to these types of stresses is then detailed. The analysis takes into account the uncertainty factor, designed to cover uncertainties related to the real-world environment and mechanical strength, and the test factor, which takes account of the number of tests performed to demonstrate the resistance of the equipment.

Foreword to Series xiii

Introduction xvii

List of Symbols xxi

Chapter 1 Extreme Response Spectrum of a Sinusoidal Vibration 1

1.1 The effects of vibration 1

1.2 Extreme response spectrum of a sinusoidal vibration 2

1.3 Extreme response spectrum of a swept sine vibration 13

Chapter 2 Extreme Response Spectrum of a Random Vibration 21

2.1 Unspecified vibratory signal 22

2.2 Gaussian stationary random signal 23

2.3 Limit of the ERS at the high frequencies 49

2.4 Response spectrum with up-crossing risk 50

2.5 Comparison of the various formulae 62

2.6 Effects of peak truncation on the acceleration time history 66

2.7 Sinusoidalvibration superimposed on a broadband random vibration 68

2.8 Swept sine superimposed on a broadband random vibration 83

2.9 Swept narrowbands on a wideband random vibration 85

Chapter 3 Fatigue Damage Spectrum of a Sinusoidal Vibration 89

3.1 Fatigue damage spectrum definition 89

3.2 Fatigue damage spectrum of a single sinusoid 92

3.3 Fatigue damage spectum of a periodic signal 96

3.4 General expression for the damage 98

3.5 Fatigue damage with other assumptions on the S-N curve 98

3.6 Fatigue damage generated by a swept sine vibration on a single-degree-of-freedom linear system 102

3.7 Reduction of test time 121

3.8 Notes on the design assumptions of the ERS and FDS 124

Chapter 4 Fatigue Damage Spectrum of a Random Vibration 125

4.1 Fatigue damage spectrum from the signal as function of time 125

4.2 Fatigue damage spectrum derived from a power spectral density 127

4.3 Simplified hypothesis of Rayleigh's law 132

4.4 Calculation of the fatigue damage spectrum with Dirlik's probability density 138

4.5 Up-crossing risk fatigue damage spectrum 140

4.6 Reduction of test time 144

4.7 Truncation of the peaks of the "input" acceleration signal 149

4.8 Sinusoidal vibration superimposed on a broadband random vibration 152

4.9 Swept sine superimposed on a broadband random vibration 161

4.10 Swept narrowbands on a broadband random vibration 162

Chapter 5 Fatigue Damage Spectrum of a Shock 165

5.1 General relationship of fatigue damage 165

5.2 Use of shock response spectrum in the impulse zone 167

5.3 Damage created by simple shocks in static zone of the response spectrum 169

Chapter 6 Influence of Calculation Conditions of ERSs and FDSs 171

6.1 Variation of the ERS with amplitude and vibraiton duration 171

6.2 Variation of the FDS with amplitude and duration of vibration 175

6.3 Should ERSs and FDSs be drawn with a linear or logarithmic frequency step? 175

6.4 With how many points must ERSs and FDSs be calculated? 177

6.5 Difference between ERSs and FDSs calculated from a vibratory signal according to time and from its PSD 180

6.6 Influence of the number of PSD calculation points on ERS and FDS 187

6.7 Influence of the PSD statistical error on ERS and FDS 192

6.8 Influence of the sampling frequency during ERS and FDS calculation from a signal on time 193

6.9 Influence of the peak counting method 202

6.10 Influence of a non-zero mean stress on FDS 206

Chapter 7 Tests and Standards 217

7.1 Definitions 217

7.2 Types of tests 218

7.3 What can be expected from a test specification? 223

7.4 Specification types 224

7.5 Standards specifying test tailoring 235

Chapter 8 Uncertainty Factor 243

8.1 Need - definitions 243

8.2 Sources of uncertainty 247

8.3 Statistical aspect of the real environment and of material strength 249

8.4 Statistical uncertainty factor 272

Chapter 9 Aging Factor 293

9.1 Purpose of the aging factor 293

9.2 Aging functions used in reliability 293

9.3 Method for calculating the aging factor 296

9.4 Influence of the aging law's standard deviation 299

9.5 Influence of the aging law mean 300

Chapter 10 Test Factor 301

10.1 Philosophy 301

10.2 Normal distributions 303

10.3 Log-normal distributions 315

10.4 Weibull distributions 318

10.5 Choice of confidence level 320

Chapter 11 Specification Development 321

11.1 Test tailoring 321

11.2 Step 1: analysis of the life-cycle profile. Review of the situations 322

11.3 Step 2: determination of the real environmental data associated with each situation 324

11.4 Step 3: determination of the environment to be simulated 325

11.5 Step 4: establishment of the test program 356

11.6 Applying this method ot the example of the "round robin" comparative study 363

11.7 Taking environment into account in project mamagement 366

Chapter 12 Influence of Calculation Conditions of Specification 375

12.1 Choice of the number of points in the specification (PSD) 375

12.2 Influence of the Q factor on specification (outside of time reduction) 378

12.3 Influence of the Q factor on specification when duration id reduced 382

12.4 Validity of a specification established for a Q factor equal to 10 when the real structure has another value 387

12.5 Advantage in the consideration of a variable Q factor for the calculation of ERSs and FDSs 388

12.6 Influence of the value of parameter b on the specification 390

12.7 Choice of the value of parameter b in the case of material made up of several components 394

12.8 Influence of temperature on parameter b and constant C  395

12.9 Importance of a factor of 10 between the specification FDS and the reference FDS (real environment) in a small frequency band 396

12.10 Validity of a specification  established by reference to a one-degree-of-freedom system when real structures are multi-degree-of-freedom systems 398

Chapter 13 OPther Uses of Extreme Response, Up-Crossing Risk and Fitigue Damage Spectra 399

13.1 Comparisons of the severity of different vibrations 399

13.2 Swept sine excitation - random vibration transformation 403

13.3 Definition of a random vibration with the same severity as a series of shocks 408

13.4 Writing a specification only from an ERS (or an URS) 413

13.5 Establishment of a swept sine vibration specification 418

Appendix 421

Formulae 457

Bibliography 481

Index 497