9780673980526

Structural Dynamics Theory and Applications

by ; ;
  • ISBN13:

    9780673980526

  • ISBN10:

    0673980529

  • Edition: 1st
  • Format: Paperback
  • Copyright: 12/1/1998
  • Publisher: Pearson

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Supplemental Materials

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  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
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Summary

The dynamic analysis of complex structures has experienced impressive progress since the 1970s. Among the reasons for this trend are the advent of digital computers and the development of sophisticated numerical analysis tools, particularly the finite element method. As technologies in these areas continue to advance, practical dynamic analyses, both linear and nonlinear, of extremely complicated systems are becoming more commonplace. Therefore, it is imperative that engineers familiarize themselves with these modern numerical solution techniques and their implementation on digital computers.

The motivation for this book is to provide engineers with an understanding of the dynamic response of structures and of the common analysis techniques employed to evaluate these responses. Although the book emphasizes numerical solution techniques for a range of applications in structural dynamics, a comprehensive treatment of the classical analytical methods is also included. Among the special topics addressed in the book are the response of structures to earthquake excitation, the analysis of blast loading, wave forces on structures, wave propagation in elastic media, and nonlinear dynamic response. Moreover, the solution techniques demonstrated throughout the text are versatile and not limited to these topics, and are appropriate for many other applications in civil, mechanical, and aerospace engineering.

The book contains material for several courses on structural dynamics. The material includes a wide range of subjects, from very elementary to advanced, arranged in increasing order of difficulty. To systematize presentation of the material, the book is organized into five parts: I. Single-Degree-of-Freedom (SDOF) Systems; II. Multi-Degree-of-Freedom (MDOF) Systems; III. Continuous Systems; IV. Nonlinear Dynamic Response; and V. Practical Applications. The material in Part I is suitable for an elementary introductory course in structural dynamics at the junior or senior level. A more comprehensive course in introductory structural dynamics, taught to advanced seniors and first-year graduate students, can be offered from the material in Parts I and II. An advanced graduate level course in structural dynamics can include the material in Parts III and IV, and several selected topics from Part V.

Throughout the book, detailed derivations and implementation of numerical solution techniques are presented. Indeed, many of the end-of-chapter homework problems require a PC computer solution. Depending on a studentís level of sophistication, they may write their own computerroutines or use commercially available software packages such as Matlab, MATHCAD, and MAPLE to solve the problems. As a convenience, a suite of computer programs written in FORTRAN for a PC that may be employed for the problem solutions are available on the authors' website at http://www.Structural-Dynamics.com.

This book has been written to serve not only as a textbook for college and university students, but also as a reference book for practicing engineers. The analytical formulations and numerical solution techniques presented throughout the book underlie most computer programs used by engineers in analyzing and designing structures subject to dynamic loadings.

The contents of this book are the result of teaching courses in structural dynamics and wave mechanics at Auburn University, Oregon State University and the University of Florida. The content was strongly influenced by our research experience. Organizations that have supported our research include the Air Force Office of Scientific Research, U.S. Army Corps of Engineers Waterways Experiment Station, Wright Laboratory Armament Directorate, Wright Laboratory Air Base Survivability Section, Office of Naval Research, SeaGrant, the Federal Highway Administration, and the Alabama Department of Transportation. We are indebted to the colleagues with whom we worked at these organizations.

We are very appreciative to the following individuals for their careful reviews of the manuscript and for their constructive suggestions: Thomas Baker, University of Virginia; James F. Doyle, Purdue University; Faoud Fanos, Iowa State University; Winfred A. Foster, Auburn University; Ronald B. Guenther, Oregon State University; Robert T. Hudspeth, Oregon State University; Barry T. Rosson, University of Nebraska; Parthe Sakar, Texas Tech University; Avi Singhal, Arizona State University; Bozidar Stojadinovic, University of Michigan; Theodore Toridis, George Washington University; Penny Vann, Texas Tech University; A. Neil Williams, University of Houston; Solomon C.S. Yim, Oregon State University; and Norimi Mitzutani, Nagoya University. We are also thankful to many former students who assisted in the solutions of the in-text examples and the end-of-chapter homework exercises, especially Mahmoud El-Mihilmy, Sanjoy Chakraborty, Prabhakar Marur, Dennis Tow, Johnathan Powell, Molly Hughes, Nathan Porter, and Robert Williams.

Joseph W. Tedesco
William G. McDougal
C. Allen Ross

Author Biography

C. Allen Ross is Emeritus Professor of the Department of Aerospace Engineering, Mechanics and Engineering Science at the University of Florida, and is a faculty member at the Graduate Engineering Research Center, Shalimar, Florida. Dr. Ross is a Registered Professional Engineer with the State of Florida and has thirty-eight years of teaching and research experience with the University of Florida. He serves on a number of professional committees and is an Associate Fellow of AIAA.

Table of Contents

Preface ix
Basic Concepts
1(12)
Introduction to Structural Dynamics
1(1)
Types of Dynamic Loads
2(1)
Sources of Dynamic Loads
2(2)
Distinguishing Features of a Dynamic Problem
4(1)
Methodology for Dynamic Analysis
5(4)
Types of Structural Vibration
9(1)
Organization of the Text
10(2)
Systems of Units
12(1)
References
12(1)
PART I Single-Degree-of-Freedom (SDOF) Systems 13(222)
Equation of Motion and Natural Frequency
15(30)
Fundamental Components of a Vibrating System
15(1)
D'Alembert's Principle of Dynamic Equilibrium
16(5)
The Energy Method
21(3)
The Principle of Virtual Displacements
24(16)
References
40(1)
Notation
40(1)
Problems
40(5)
Undamped Free Vibration
45(33)
Simple Harmonic Motion
45(5)
Interpretation of the Solution
50(6)
Equivalent Stiffness
56(10)
Rayleigh Method
66(5)
References
71(1)
Notation
72(1)
Problems
72(6)
Damped Free Vibration
78(27)
Free Vibration with Viscous Damping
78(8)
Logarithmic Decrement
86(5)
Hysteresis Damping
91(5)
Coulomb Damping
96(4)
References
100(1)
Notation
100(1)
Problems
101(4)
Response to Harmonic Excitation
105(35)
Forced Harmonic Response of Undamped Systems
105(5)
Beating and Resonance
110(6)
Forced Harmonic Vibrations with Viscous Damping
116(5)
Effect of Damping Factor on Steady-State Response and Phase Angle
121(4)
Harmonic Excitation Caused by Rotating Unbalance
125(3)
Base Excitation
128(3)
Vibration Isolation and Transmissibility
131(4)
References
135(1)
Notation
135(1)
Problems
136(4)
Response to Periodic and Arbitrary Dynamic Excitation
140(32)
Response to Periodic Excitation
140(8)
Response to Unit Impulse
148(2)
Duhamel Integral
150(1)
Response to Arbitrary Dynamic Excitation
151(11)
Response Spectrum
162(4)
References
166(1)
Notation
167(1)
Problems
167(5)
Numerical Evaluation of Dynamic Response
172(35)
Interpolation of the Excitation
172(5)
Direct Integration of the Equation of Motion
177(1)
Central Difference Method
177(6)
Runge-Kutta Methods
183(6)
Average Acceleration Method
189(5)
Linear Acceleration Method
194(4)
Response to Base Excitation
198(4)
Response Spectra by Numerical Integration
202(2)
References
204(1)
Notaion
204(1)
Problems
205(2)
Frequency Domain Analysis
207(28)
Alternative Forms of the Fourier Series
207(7)
Discrete Fourier Transform
214(3)
Fast Fourier Transform
217(6)
Discrete Fourier Transform Implementation Considerations
223(6)
Fourier Intergral
229(3)
References
232(1)
Notation
232(1)
Problems
233(2)
PART II Muti-Degree-of-Freedom (MDOF) Systems 235(200)
General Property Matrices for Vibrating Systems
237(41)
Flexibility Matrix
237(6)
Stiffness Matrix
243(9)
Inertia Properties: Mass Matrix
252(3)
The Eigenproblem in Vibration Analysis
255(6)
Static Condensation of the Stiffness Matrix
261(10)
References
271(1)
Notation
271(1)
Problems
272(6)
Equations of Motion and Undamped Free Vibration
278(49)
Hamilton's Principle and the Lagrange Equations
279(9)
Natural Vibration Frequencies
288(2)
Natural Vibration Modes
290(6)
Orthogonality of Natural Modes
296(1)
Systems Admitting Rigid-Body Modes
297(7)
Generalized Mass and Stiffness Matrics
304(4)
Free Vibration Response to Initial Conditions
308(6)
Approximate Methods for Estimating the Fundamental Frequency
314(7)
References
321(1)
Notation
321(1)
Problems
322(5)
Numerical Solution Methods for Natural Frequencies and Mode Shapes
327(30)
General Solution Methods for Eigenproblems
327(2)
Inverse Vector Iteration
329(10)
Forward Vector Iteration
339(5)
Generalized Jacobi Method
344(8)
Solution Methods for Large Eigenproblems
352(1)
References
353(1)
Notation
353(1)
Problems
354(3)
Analysis of Dynamic Response by Mode Superposition
357(41)
Mode Displacement Method for Undamped Systems
357(9)
Modal Participation Factor
366(3)
Mode Superposition Solution for Solution for Systems with Classical Damping
369(4)
Numerical Evaluation of Modal Response
373(5)
Normal Mode Response to Support Motions
378(6)
Response Spectrum Analysis
384(2)
Mode Acceleration Method
386(5)
References
391(1)
Notation
392(1)
Problems
393(5)
Analysis of Dynamic Response by Direct Integration
398(37)
Basic Concepts of Direct Integration Methods
398(1)
The Central Difference Method
399(8)
The Wilson-θ Method
407(10)
The Newmark Method
417(3)
Practical Considerations for Damping
420(7)
Stability and Accuracy of Direct Integration Methods
427(1)
Direct Integration Versus Mode Superposition
428(1)
Referenreces
429(1)
Notation
430(1)
Problems
431(4)
PART III Continuous Systems 435(60)
Vibrations of Continuous Systems
437(58)
Longitudinal Vibration of a Uniforms Rod
438(5)
Transverse Vibration of a Pretensioned Cable
443(2)
Free Transverse Vibration of Uniform Beams
445(13)
Orthogonality of Normal Modes
458(2)
Undamped Forced Vibration of Beams by Mode Superposition
460(7)
Approximate Methods
467(21)
References
488(1)
Notation
488(1)
Problems
489(6)
PART IV Nonlinear Dynamic Response 495(54)
Analysis of Nonlinear Response
497(52)
Classification of Nonlinear Analyses
498(5)
Systems With Nonlinear Characteristics
503(3)
Formulation of Incremental Equations of Equilibrium
506(2)
Numerical Solution of Nonlinear Equilibrium Equations
508(9)
Response of Elastoplastic SDOF Systems
517(15)
Repsonse of Elastoplastic MDOF Systems
532(12)
References
544(1)
Notation
544(2)
Problems
546(3)
PART V Practical Applications 549(248)
Elastic Wave Propagation in Solids
551(33)
Stress and Strain at a Point
552(3)
Constitutive Relations
555(8)
Equations of Motion
563(1)
Stress Wave Propagation
563(8)
Applications
571(11)
References
582(1)
Problems
583(1)
Earthquakes and Earthquake Ground Motion
584(17)
Causes of Earthquakes
584(2)
Faults
586(1)
Seismic Waves
587(2)
Earthquake Intensity
589(3)
Earthquake Magnitude
592(2)
Seismicity
594(2)
Earthquake Ground Motion
596(3)
Earthquake Damage Mechanisms
599(1)
References
599(1)
Notation
600(1)
Earthquake Response of Structures
601(81)
Time-History Analysis: Basic Concepts
602(8)
Earthquake Response Spectra
610(6)
Earthquake Design Spectra
616(16)
Response of MDOF Systems
632(16)
Generalized SDOF Systems
648(12)
In-Building Response Spectrum
660(5)
Inelastic Response
665(8)
Seismic Design Codes
673(2)
References
675(1)
Notation
676(2)
Problems
678(4)
Blast Loads on Structures
682(28)
Sources of Blast Loads
682(1)
Shock Waves
683(6)
Determination of Blast Loads
689(6)
Strain-Rate Effects
695(6)
Approximate Solution Technique for SDOF Systems
701(5)
Refereces
706(1)
Problems
707(1)
Notations
708(2)
Basic Concepts of Wind Waves
710(42)
Linear Wave Theory
710(9)
Nonlinear Waves
719(3)
Wave Transformations
722(8)
Wave Statistics
730(11)
Wave Information Damping
741(7)
References
748(1)
Notation
749(1)
Problems
750(2)
Response of Structures to Waves
752(45)
Morison Equation
753(7)
Force Coefficients
760(8)
Linearized Morison Equation
768(4)
Inclined Cylinders
772(4)
Transverse Lift Forces
776(2)
Froude-Krylov Theory
778(1)
Diffraction Theory: The Scattering Problem
779(9)
Diffraction Theory: The Radiation Problem
788(6)
References
794(1)
Notation
794(1)
Problems
795(2)
Appendix A 797(2)
Appendix B 799(2)
Index 801

Excerpts

The dynamic analysis of complex structures has experienced impressive progress since the 1970s. Among the reasons for this trend are the advent of digital computers and the development of sophisticated numerical analysis tools, particularly the finite element method. As technologies in these areas continue to advance, practical dynamic analyses, both linear and nonlinear, of extremely complicated systems are becoming more commonplace. Therefore, it is imperative that engineers familiarize themselves with these modern numerical solution techniques and their implementation on digital computers.The motivation for this book is to provide engineers with an understanding of the dynamic response of structures and of the common analysis techniques employed to evaluate these responses. Although the book emphasizes numerical solution techniques for a range of applications in structural dynamics, a comprehensive treatment of the classical analytical methods is also included. Among the special topics addressed in the book are the response of structures to earthquake excitation, the analysis of blast loading, wave forces on structures, wave propagation in elastic media, and nonlinear dynamic response. Moreover, the solution techniques demonstrated throughout the text are versatile and not limited to these topics, and are appropriate for many other applications in civil, mechanical, and aerospace engineering.The book contains material for several courses on structural dynamics. The material includes a wide range of subjects, from very elementary to advanced, arranged in increasing order of difficulty. To systematize presentation of the material, the book is organized into five parts: I. Single-Degree-of-Freedom (SDOF) Systems; II. Multi-Degree-of-Freedom (MDOF) Systems; III. Continuous Systems; IV. Nonlinear Dynamic Response; and V. Practical Applications. The material in Part I is suitable for an elementary introductory course in structural dynamics at the junior or senior level. A more comprehensive course in introductory structural dynamics, taught to advanced seniors and first-year graduate students, can be offered from the material in Parts I and II. An advanced graduate level course in structural dynamics can include the material in Parts III and IV, and several selected topics from Part V.Throughout the book, detailed derivations and implementation of numerical solution techniques are presented. Indeed, many of the end-of-chapter homework problems require a PC computer solution. Depending on a student's level of sophistication, they may write their own computerroutines or use commercially available software packages such as Matlab, MATHCAD, and MAPLE to solve the problems. As a convenience, a suite of computer programs written in FORTRAN for a PC that may be employed for the problem solutions are available on the authors' website at http://www.Structural-Dynamics.com .This book has been written to serve not only as a textbook for college and university students, but also as a reference book for practicing engineers. The analytical formulations and numerical solution techniques presented throughout the book underlie most computer programs used by engineers in analyzing and designing structures subject to dynamic loadings.The contents of this book are the result of teaching courses in structural dynamics and wave mechanics at Auburn University, Oregon State University and the University of Florida. The content was strongly influenced by our research experience. Organizations that have supported our research include the Air Force Office of Scientific Research, U.S. Army Corps of Engineers Waterways Experiment Station, Wright Laboratory Armament Directorate, Wright Laboratory Air Base Survivability Section, Office of Naval Research, SeaGrant, the Federal Highway Administration, and the Alabama Departmen

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