Table of contents for Structural dynamics and probabilistic analyses for engineers / Giora Maymon.


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CHAPTER
1   Some Basics of the Theory of Vibrations                      1
1.1  A Single Degree of Freedom System                       1
1.2  Response of a SDOF to (Any) Transient Load              7
1.3  Multiple-Degrees-of-Freedom (MDOF) System              11
1.4  Infinite-Degrees-of-Freedom (Continuous) System        18
1.5  Mounted Mass                                           19
CHAPTER
2   Dynamic Response of Beams and Other Structures
to Deterministic Excitation                                 21
2.1  A Generic Example of a Cantilever Beam                 21
2.2  Some Basics of the Slender Beam Theory                 21
2.3  Modal Analysis of a Slender Cantilever Beam            25
2.4  Stress Modes of a Slender Cantilever Beam              29
2.5  Response of a Slender Beam to Harmonic Excitation      35
2.5.1  Response of beams to base excitation             37
2.5.2  Response of a cantilever beam to harmonic tip force  38
2.5.3  Response of a cantilever beam to harmonic base excitation  41
2.5.4  Two external forces                              44
2.6  Response of a Structure with Mounted Mass to Harmonic
Excitation                                           45
2.7  Symmetric and Anti-symmetric Modes and Loads        52
2.8  Response of a Simply Supported Plate to Harmonic
Excitation                                           57
2.9  Vibrations of Shells                                66
CHAPTER
3   Dynamic Response of a Structure to Random Excitation    70
3.1  Random Excitation and Response                      70
3.2  Response of an Elastic Structure to Random Excitation  78
3.2.1  Closed form solution                          85
3.3  Response of a Cantilever Beam to Clamp Displacement
Excitation                                           88
3.4  Response of a Cantilever Beam to Tip Displacement
Excitation                                           92
3.5  Simulation of an Important Structural Parameter
in a Vibration Test                                  96
3.5.1  Two examples                                  97
3.6  Response of a Structure to Acoustic Excitation      116
3.7  An Example of a Frame Structure                    125
3.8  Response of a Structure with Mounted Mass to Random
Excitation                                          132
3.9  Response of a Simply Supported Plate to Random
Excitation                                          140
CHAPTER
4  Contacts In Structural Systems                          146
4.1  Static Contact                                      146
4.1.1 An example of a static contact problem        147
4.2  Analytical Solution for a Dynamic Contact Problem   150
4.3  The Two DOF Contact Problem                         157
4.4  Numerical Solution of a Dynamic Contact
Problem-Force Excitation                            162
4.5  Numerical Solution of a Dynamic Contact
Problem-Base Excitation                             167
CHAPTER
5   Nondeterministic Behavior of Structures                       173
5.1  Probabilistic Analysis of Structures                      173
5.1.1  The basic stress-strength case                     177
5.2  Solutions for the Probability of Failure                  180
5.2.1  Analytical solution-the Lagrange multiplier method  180
5.2.2  The monte carlo simulation                         183
5.2.3  Solution with a probabilistic analysis program     184
5.2.4  Solutions for cases where no closed-form expressions exist  185
5.3  Solution with a Commercial Finite Element Program         191
5.4  Probability of Failure of Dynamically Excited Structures  192
5.5  Structural Systems                                        198
5.6  Model Uncertainties                                       208
CHAPTER
6   Random Crack Propagation                                      217
6.1  Crack Propagation in a Structural Element                 217
6.2  Effects of a Static Bias on the Dynamic Crack Growth      223
6.3  Stochastic Crack Growth and the Probability of Failure
for Harmonic Excitation                                   228
6.4  Initial Cracks and Flaws                                  237
6.5  Probabilistic Crack Growth Using the "Unified"
Approach                                                  246
6.6  Stochastic Crack Growth and the Probability of Failure
for Random Excitation                                     266
CHAPTER
7   Design Criteria                                               275
7.1  Dynamic Design Criteria                                   275
7.1.1  Case of under-design                               276
7.1.2  Case of over-design                                277
7.2  The Factor of Safety                                      283
7.2.1  Factor of safety                                   283
7.3  Reliability Demonstration of Structural Systems           289
7.3.1  Reliability demonstration (verification) is integrated into
the design process                                  293
7.3.2  Analysis of failure mechanism and failure modes      293
7.3.3 Modeling the structural behavior; and verifying the model
by tests                                             294
7.3.4 Design of structural development tests to surface failure
modes                                                294
73.5  Design of structural development tests to surface
unpredicted failure modes                            295
73.6  "Cleaning"failure mechanism and failure modes         295
73.7  Determination of the required safety margins, the
confidence in the models and the relevant parameters  296
73.8  Determination of the demonstrated reliability by "orders of
magnitude"                                           296
CHAPTER
8   Some Important Computer Programs for Structural Analysis        300
8.1   Finite Elements Programs                                   300
8.2   Probabilistic Analysis Programs                            301
8.3  Crack Propagation Programs                                  304
8.4  Mathematical Solvers                                        305
CHAPTER
9 Conclusions-Do and Don't Do in Dynamic and Probabilistic
Analyses                                                        307
APPENDIX
Computer Files for the Demonstration Problems                   313
1    Introduction                                                313
2    List of Files                                               314
3    Files Listing                                               317
References                                                         420
Index                                                              427



Library of Congress subject headings for this publication: Structural dynamics, Structural analysis (Engineering)Probabilities