Structural Dynamics and Probabilistic Analyses for Engineers

by Maymon, Giora

• ISBN13: 9780750687652
• ISBN10: 0750687657
• Edition: CD
• Format: Hardcover
• Copyright: 2008-05-29
• Publisher: Butterworth-Heinemann

Summary

Probabilistic structural dynamics offers unparalleled tools for analyzing uncertainties in structural design. Once avoided because it is mathematically rigorous, this technique has recently remerged with the aide of computer software. Written by an author/educator with 40 years of experience in structural design, this user friendly manual integrates theories, formulas and mathematical models to produce a guide that will allow professionals to quickly grasp concepts and start solving problems. In this book, the author uses simple examples that provide templates for creating of more robust case studies later in the book. *Problems are presented in an easy to understand form *Practical guide to software programs to solve design problems *Packed with examples and case studies of actual projects *Classical and the new stochastic factors of safety

Table of Contents

List of Figures	p. xiii
List of Tables	p. xxiii
Foreword	p. xxv
Preface	p. xxvii
Some Basics of the Theory of Vibrations	p. 1
A Single Degree of Freedom System	p. 1
Response of a SDOF to (Any) Transient Load	p. 7
Multiple-Degrees-of-Freedom (MDOF) System	p. 11
Infinite-Degrees-of-Freedom (Continuous) System	p. 18
Mounted Mass	p. 19
Dynamic Response of Beams and Other Structures to Deterministic Excitation	p. 21
A Generic Example of a Cantilever Beam	p. 21
Some Basics of the Slender Beam Theory	p. 21
Modal Analysis of a Slender Cantilever Beam	p. 25
Stress Modes of a Slender Cantilever Beam	p. 29
Response of a Slender Beam to Harmonic Excitation	p. 35
Response of beams to base excitation	p. 37
Response of a cantilever beam to harmonic tip force	p. 38
Response of a cantilever beam to harmonic base excitation	p. 41
Two external forces	p. 44
Response of a Structure with Mounted Mass to Harmonic Excitation	p. 45
Symmetric and Anti-symmetric Modes and Loads	p. 52
Response of a Simply Supported Plate to Harmonic Excitation	p. 57
Vibrations of Shells	p. 66
Dynamic Response of a Structure to Random Excitation	p. 70
Random Excitation and Response	p. 70
Response of an Elastic Structure to Random Excitation	p. 78
Closed form solution	p. 85
Response of a Cantilever Beam to Clamp Displacement Excitation	p. 88
Response of a Cantilever Beam to Tip Displacement Excitation	p. 92
Simulation of an Important Structural Parameter in a Vibration Test	p. 96
Two examples	p. 97
Response of a Structure to Acoustic Excitation	p. 116
An Example of a Frame Structure	p. 125
Response of a Structure with Mounted Mass to Random Excitation	p. 132
Response of a Simply Supported Plate to Random Excitation	p. 140
Contacts In Structural Systems	p. 146
Static Contact	p. 146
An example of a static contact problem	p. 147
Analytical Solution for a Dynamic Contact Problem	p. 150
The Two DOF Contact Problem	p. 157
Numerical Solution of a Dynamic Contact Problem-Force Excitation	p. 162
Numerical Solution of a Dynamic Contact Problem-Base Excitation	p. 167
Nondeterministic Behavior of Structures	p. 173
Probabilistic Analysis of Structures	p. 173
The basic stress-strength case	p. 177
Solutions for the Probability of Failure	p. 180
Analytical solution-the Lagrange multiplier method	p. 180
The monte carlo simulation	p. 183
Solution with a probabilistic analysis program	p. 184
Solutions for cases where no closed-form expressions exist	p. 185
Solution with a Commercial Finite Element Program	p. 191
Probability of Failure of Dynamically Excited Structures	p. 192
Structural Systems	p. 198
Model Uncertainties	p. 208
Random Crack Propagation	p. 217
Crack Propagation in a Structural Element	p. 217
Effects of a Static Bias on the Dynamic Crack Growth	p. 223
Stochastic Crack Growth and the Probability of Failure for Harmonic Excitation	p. 228
Initial Cracks and Flaws	p. 237
Probabilistic Crack Growth Using the "Unified" Approach	p. 246
Stochastic Crack Growth and the Probability of Failure for Random Excitation	p. 266
Design Criteria	p. 275
Dynamic Design Criteria	p. 275
Case of under-design	p. 276
Case of over-design	p. 277
The Factor of Safety	p. 283
Factor of safety	p. 283
Reliability Demonstration of Structural Systems	p. 289
Reliability demonstration (verification) is integrated into the design process	p. 293
Analysis of failure mechanism and failure modes	p. 293
Modeling the structural behavior, and verifying the model by tests	p. 294
Design of structural development tests to surface failure modes	p. 294
Design of structural development tests to surface unpredicted failure modes	p. 295
"Cleaning" failure mechanism and failure modes	p. 295
Determination of the required safety margins, the confidence in the models and the relevant parameters	p. 296
Determination of the demonstrated reliability by "orders of magnitude"	p. 296
Some Important Computer Programs for Structural Analysis	p. 300
Finite Elements Programs	p. 300
Probabilistic Analysis Programs	p. 301
Crack Propagation Programs	p. 304
Mathematical Solvers	p. 305
Conclusions-Do and Don't Do in Dynamic and Probabilistic Analyses	p. 307
Computer Files for the Demonstration Problems	p. 313
Introduction	p. 313
List of Files	p. 314
Files Listing	p. 317
References	p. 420
Index	p. 427
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