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Random vibrations : theory and practice

Random vibrations : theory and practice (Loan 2 times)

Material type
단행본
Personal Author
Wirsching, Paul H. Paez, Thomas L., 1949- Ortiz, Keith.
Title Statement
Random vibrations : theory and practice / Paul H. Wirsching, Thomas L. Paez, Keith Ortiz.
Publication, Distribution, etc
New York :   John Wiley & Sons,   c1995.  
Physical Medium
xvi, 448 p. : ill. ; 25 cm.
ISBN
0471585793 (cloth : alk. paper)
General Note
"A Wiley-Interscience Publication."  
Bibliography, Etc. Note
Includes bibliographical references (p. 433-440) and index.
Subject Added Entry-Topical Term
Random vibration.
000 00845pamuuu200265 a 4500
001 000000478096
003 OCoLC
005 19970424155441.0
008 950616s1995 nyua b 001 0 eng
010 ▼a 95032229
020 ▼a 0471585793 (cloth : alk. paper)
040 ▼a DLC ▼c DLC
049 ▼a ACSL ▼l 121023970
050 0 0 ▼a TA355 ▼b .W57 1995
082 0 0 ▼a 620.3 ▼2 20
090 ▼a 620.3 ▼b W798r
100 1 ▼a Wirsching, Paul H.
245 1 0 ▼a Random vibrations : ▼b theory and practice / ▼c Paul H. Wirsching, Thomas L. Paez, Keith Ortiz.
260 ▼a New York : ▼b John Wiley & Sons, ▼c c1995.
300 ▼a xvi, 448 p. : ▼b ill. ; ▼c 25 cm.
500 ▼a "A Wiley-Interscience Publication."
504 ▼a Includes bibliographical references (p. 433-440) and index.
650 0 ▼a Random vibration.
700 1 ▼a Paez, Thomas L., ▼d 1949-
700 1 ▼a Ortiz, Keith.

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 620.3 W798r Accession No. 121023970 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents


CONTENTS
Preface = xv
1 Introduction = 1
 1.1 History and Motivation = 1
 1.2 Example = 4
 1.3 Scope and Organization = 6
2 Random Variables = 9
 2.1 Essential Probability = 9
  2.1.1 Set Theory = 10
  2.1.2 Axioms of Probability = 11
  2.1.3 Conditional Probability and Independence = 12
 2.2 Single Random Variables = 14
  2.2.1 Discrete Random Variables and Probability Mass Function = 14
  2.2.2 Continuous Random Variables and Probability Density Function = 15
  2.2.3 Cumulative Distribution Functions = 19
  2.2.4 Measures of Central Tendency and Dispersion = 21
  2.2.5 Expected Values = 23
  2.2.6 Moment-Generating Functions = 25
  2.2.7 Gaussian (Normal) Random Variables = 26
 2.3 Jointly Distributed Random Variables = 30
  2.3.1 Joint and Marginal Distributions = 30
  2.3.2 Conditional Distributions and Independence = 33
  2.3.3 Expected Values, Covariance and Correlation Coefficient = 36
  2.3.4 Linear Dependence = 38
  2.3.5 Joint Normal Distribution = 41
 2.4 Function of Random Variables = 43
  2.4.1 Change of Variables by Cumulative Distribution Function = 43
  2.4.2 Change of Variables by Probability Density Function = 45
  2.4.3 Multidimensional Change of Variables = 49
  2.4.4 Sums of Random Variables = 51
 2.5 Central Limit Theorem and Distributions Related to Normal Distribution = 55
  2.5.1 De Moivre-Laplace Approximation = 56
  2.5.2 Central Limit Theorem = 57
  2.5.3 Distribution of Sample Mean: Normal = 58
  2.5.4 Distribution of Sample Variance: Chi Squared = 60
  2.5.5 Distributions of Related Ratios of Random Variables: t and F = 64
  2.5.6 Distribution of Extreme Values = 65
Problems = 68
3 Random Processes in Time Domain = 72
 3.1 Random Process Definitions = 72
  3.1.1 State Spaces and Index Sets = 72
  3.1.2 Ensembles and Ensemble Averages = 73
  3.1.3 Stationary Processes = 80
  3.1.4 Ergodic Processes = 82
  3.1.5 Gaussian Processes = 83
 3.2 Correlation = 84
  3.2.1 Characteristics of Autocorrelation Function = 84
  3.2.2 Cross-Correlation Function and Linear Transformations = 86
  3.2.3 Derivatives of Stationary Processes = 89
 3.3 Some Essential Random Processes = 91
  3.3.1 Harmonic Processes = 91
  3.3.2 Poisson Process = 94
Problems = 96
4 Fourier Transforms = 100
 4.1 Fourier Transform = 100
  4.1.1 Fourier Series = 101
  4.1.2 Fourier Transforms = 104
  4.1.3 Symmetry = 107
  4.1.4 Basic Theorems = 108
  4.1.5 Correlation, Convolution, and Windowing = 111
 4.2 Dirac Delta Function = 113
  4.2,1 Definition and Properties of Delta Function = 113
  4.2.2 Fourier Transform of Delta Function = 116
  4.2.3 Transforms of Cosine and Sine Functions = 118
Problems = 119
5 Random Processes in Frequency Domain = 123
 5,1 Spectral Density Function = 123
  5.1.1 Definition = 124
  5.1.2 Relationship with Fourier Transform of X(t) = 127
  5.1.3 Practical Issues = 130
  5.1.4 White Noise and Bandpass Filtered Spectra = 135
 5.2 Cross-Spectral Density Function = 139
  5.2.1 Definition = 139
  5.2.2 Coherence Function and Linear Transformations = 140
  5.2.3 Derivatives of Stationary Processes = 141
Problems = 143
6 Statistical Properties of Random Processes = 146
 6.1 Level Crossings = 146
  6.1.1 Preliminary Remarks = 146
  6.1.2 Derivation of Expected Rate of Level Crossing = 150
  6.1.3 Specializations = 152
  6.1.4 Rice's Narrow-Band Envelope = 157
 6.2 Distributions of Extrema = 162
  6.2.1 Simple Approach to Distribution of Peak = 162
  6.2.2 General Approach to Distribution of Peak = 164
  6.2.3 Approximate Distribution for Height of Rise or Fall = 167
Problems = 171
7 Vibration of Single-Degree-of-Freedom Systems = 174
 7.1 Free Vibration of Single-Degree-of-Freedom System = 174
  7.1.1 Background = 174
  7.1.2 Harmonic Motion = 174
  7.1.3 Free Vibration of Undamped Single-Degree-of-Freedom System = 177
  7.1.4 Damped Free Vibration of Single-Degree-of-Freedom System = 179
 7.2 Forced Vibration = 180
  7.2.1 Force-Excited System: Harmonic Excitation = 180
  7.2.2 Base-Excited System: Absolute Motion = 183
  7.2.3 Base-Excited System: Relative Motion = 184
 7.3 Background for Response of Single-Degree-of-Freedom System to Random Forces = 190
  7.3.1 Response of Single-Degree-of-Freedom System to Impulsive Forces = 190
  7.3,2 Response of Single-Degree-of-Freedom System to Arbitrary Loading = 191
  7.3.3 Relationship Between h(t) and H(w)  = 192
  7.3.4 Relationship Between X(w) and F(w) = 193
Problems = 194
8 Response of Single-Degree-of-Freedom Linear Systems to Random Environments = 197
 8.1 Response to Stationary Random Forces = 197
  8.1.1 Preliminary Remarks = 197
  8.1.2 Mean of Response Process = 198
  8.1.3 Autocorrelation of Response Process = 199
  8.1.4 Spectral Density of Response Process = 202
  8.1.5 Distribution of Response Process = 203
 8.2 White-Noise Process as Model for Force = 203
  8.2.1 Definition of Process = 203
  8.2.2 Response of Force-Excited System to White Noise = 204
  8.2.3 Engineering Significance of White-Noise Process = 206
 8.3 Examples of Response of Single-Degree-of- Freedom Systems to Random Forces = 207
Problems = 213
9 Random Vibration of Multi-Degree-of-Freedom Systems = 218
 9.1 Equations of Motion for Multi-Degree-of-Freedom System = 218
  9.1.1 Introduction = 218
  9.1.2 Equations of Motion = 220
  9.1.3 Transfer Function and Impulse Response Functions for System = 221
 9.2 Direct Model for Determining Response of MDOF System = 223
  9.2.1 Expression for Response = 223
  9.2.2 Mean Value of Response = 224
  9.2.3 Autocorrelation Function = 225
  9.2.4 Spectral Density Function of Response = 226
  9.2.5 Single Response Variable: Special Cases = 227
 9.3 Normal Mode Method = 234
  9.3.1 Preliminary Remarks = 234
  9.3.2 The Eigenvalue Problem: Free-Vibration Solution to Equations of Motion = 234
  9.3.3 Example of Eigenvalue Problem = 235
  9.3.4 Normal Mode Method: Orthogonality Conditions = 237
  9.3.5 Normal Mode Method: Equations of Motion = 241
  9.3.6 Big Payoff for Using Normal Mode Method = 242
  9.3.7 Introduction of Damping into Equations of Motion = 243
  9.3.8 Normal Mode Method: Mode Combination Problem-Some Methods = 246
  9.3.9 Example of Mode Combination Algorithm Results = 248
 9.4 Computer Codes for Analyzing MDOF Structural Systems = 249
Problems = 250
10 Design to Avoid Structural Failures Due to Random Vibration = 254
 10.1 Three-Sigma Design = 254
  10.1.1 Basic Design Criterion = 254
  10.1.2 More General Statement of Three Sigma Criterion = 256
 10.2 First-Passage Failure = 257
  10.2.1 Introductory Remarks = 257
  10.2.2 Basic Formulation of First-Passage Problem = 259
  10.2.3 First-Passage Failure: Exact Distribution of Largest in Sample of Size n Independent Peaks = 260
  10.2.4 First-Passage Failure: Use of Extreme-Value Distribution to Model Distribution of Largest Peak = 263
  10.2.5 First-Passage Failure: Determination of Design Value Using Concept of Return Period = 264
 10.3 Fatigue: An Introduction = 266
  10.3.1 Physical Process of Fatigue = 266
  10.3.2 Fatigue Strength Models = 267
  10.3.3 Miner's Rule = 271
  10.3.4 Models of Fatigue Damage Under Narrow-Band Random Stress = 274
  10.3.5 Models of Fatigue Damage Under Wide-Band Random Stresses = 283
  10.3.6 Quality of Miner's Rule = 288
Problems = 290
11 Introduction to Parameter Estimation = 296
 11.1 Estimation and Analysis of Mean = 297
  11.1.1 Maximum Likelihood Estimation = 297
  11.1.2 Bias and Consistency of Mean Estimator = 301
  11.1.3 Sampling Distribution of Mean Estimator and Confidence Intervals on Mean = 303
  11.1.4 Bias in Variance Estimator = 307
 11.2 Other Important Problems in Parameter Estimation = 308
  11.2.1 Sampling Distribution for Variance = 308
  11.2.2 Confidence Intervals for Mean with Unknown Variance = 309
 11.3 Closure = 311
Problems = 312
12 Time-Domain Estimation of Random Process Parameters = 315
 12.1 Random Process Parameter Estimation via Ensemble Average = 316
  12,1.1 Mean, Variance, and Standard Deviation Function = 316
  12.1.2 Correlation = 318
  12.1.3 Autocorrelation Function = 320
  12.1.4 Cross-Correlation Function = 324
  12.1.5 Covariance and Correlation Coefficient Function = 324
 12.2 Stationary Random Process Parameter Estimation via Temporal Averaging = 325
 12.3 Other Methods for Nonstationary Random Process Analysis = 330
  12.3.1 Direct Analysis of Nonstationary Random Processes = 330
  12.3.2 Indirect Analysis of Nonstationary Random Processes: Method of Shock Response Spectra = 333
Problems = 338
13 Discrete Fourier Transform = 341
 13.1 Definition of DFT and Fundamental Characteristics = 341
 13.2 Periodicity of DFT; DFT of Real Signal = 344
 13.3 DFT of Continuous-Time Signals: Aliasing and Leakage = 350
 13.4 Data Windows = 356
 13.5 Fast Fourier Transform = 361
 13.6 Generation of Real-Valued, Finite-Duration, Sampled Realizations of Stationary, Normal Random Processes = 365
Problems = 368
14 Frequency-Domain Estimation of Random Processes = 370
 14.1 Fundamental Concepts in Estimation of Autospectral Density = 370
  14.1.1 Direct Estimation of Autospectral Density = 371
  14.1.2 Maximum Likelihood Estimation = 375
  14.1.3 Bias, Consistency, and Sampling Distribution of Autospectral Density Estimator = 378
 14.2 Practical Aspects of Estimation of Autospectral Density, '= 381
 14.3 Real-Time Estimation of Spectral Density = 386
 14.4 Estimation of Cross-Spectral Density and Ordinary Coherence = 389
  14.4.1 Cross-Spectral Density Estimation = 389
  14.4.2 Coherence Estimation = 390
  14.4.3 Bias and Consistency of Cross-Spectral Density Estimator = 391
 14.5 Estimation of Frequency Response Function = 392
  14.5.1 Frequency Response in SISO Case = 392
  14.5.2 Sampling Distribution and Variance of Frequency Response Function Estimator = 396
  14.5.3 Frequency Response Function in MISO Case = 398
Problems = 401
Appendix A Convergence of Random Processes = 404
 A.1 Introductory Comments = 404
 A.2 Modes of Convergence = 405
 A.3 Mean-Square Continuity = 407
 A.4 Mean-Square Differentiability = 407
 A.5 Mean-Square Integrability = 409
 A.6 Ergodicity = 412
 A.7 Central Limit Theorem = 413
Appendix B Integrals of Transfer Functions = 416
Appendix C Formulas for Approximate Evaluation of Some Integrals Useful in Probabili ty = 417
Appendix D Some Fast Fourier Transform Programs = 419
 D.1 C Language = 419
 D.2 Fortran = 421
Appendix E Tables = 423
 E.1 Table of Cumulative Distribution of Standard Normal Random Variable = 423
 E.2 Table of Percentage Points of X² Distribution = 426
 E.3 Table of Percentage Points of t Distribution = 429
 E.4 Table of Percentage Points of the F Distribution = 430
References = 433
Index = 441


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