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E-raamat: Advanced Structural Dynamics

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(Massachusetts Institute of Technology)
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  • Ilmumisaeg: 07-Aug-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316774168
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Advanced Structural DynamicsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 07-Aug-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316774168
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Developed from three decades' worth of lecture notes which the author used to teach at the Massachusetts Institute of Technology, this unique textbook presents a comprehensive treatment of structural dynamics and mechanical vibration. The chapters in this book are self-contained so that instructors can choose to be selective about which topics they teach. Written with an application-based focus, the text covers topics such as earthquake engineering, soil dynamics, and relevant numerical methods techniques that use MATLAB. Advanced topics such as the Hilbert transform, gyroscope forces, and spatially periodic structures are also treated extensively. Concise enough for an introductory course yet rigorous enough for an advanced or graduate-level course, this textbook is also a useful reference manual - even after the final exam - for professional and practicing engineers.

Developed from three decades' worth of lecture notes from Massachusetts Institute of Technology lectures, this concise textbook presents an exhaustive treatment of structural dynamics and mechanical vibration. Appropriate for introductory courses yet rigorous enough for advanced courses, this book is for graduate students, doctoral candidates, practicing professionals, and instructors.

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Based on the author's lectures at the Massachusetts Institute of Technology, this concise textbook presents an exhaustive treatment of structural dynamics and mechanical vibration.
Preface xxi
Notation and Symbols xxv
Unit Conversions xxix
1 Fundamental Principles 1(54)
1.1 Classification of Problems in Structural Dynamics
1(1)
1.2 Stress-Strain Relationships
2(1)
1.2.1 Three-Dimensional State of Stress-Strain
2(1)
1.2.2 Plane Strain
2(1)
1.2.3 Plane Stress
2(1)
1.2.4 Plane Stress versus Plane Strain: Equivalent Poisson's Ratio
3(1)
1.3 Stiffnesses of Some Typical Linear Systems
3(8)
1.4 Rigid Body Condition of Stiffness Matrix
11(1)
1.5 Mass Properties of Rigid, Homogeneous Bodies
12(5)
1.6 Estimation of Miscellaneous Masses
17(3)
1.6.1 Estimating the Weight (or Mass) of a Building
17(1)
1.6.2 Added Mass of Fluid for Fully Submerged Tubular Sections
18(2)
1.6.3 Added Fluid Mass and Damping for Bodies Floating in Deep Water
20(1)
1.7 Degrees of Freedom
20(2)
1.7.1 Static Degrees of Freedom
20(1)
1.7.2 Dynamic Degrees of Freedom
21(1)
1.8 Modeling Structural Systems
22(9)
1.8.1 Levels of Abstraction
22(3)
1.8.2 Transforming Continuous Systems into Discrete Ones
25(1)
Heuristic Method
25(1)
1.8.3 Direct Superposition Method
26(1)
1.8.4 Direct Stiffness Approach
26(1)
1.8.5 Flexibility Approach
27(2)
1.8.6 Viscous Damping Matrix
29(2)
1.9 Fundamental Dynamic Principles for a Rigid Body
31(8)
1.9.1 Inertial Reference Frames
31(1)
1.9.2 Kinematics of Motion
31(3)
Cardanian Rotation
32(1)
Eulerian Rotation
33(1)
1.9.3 Rotational Inertia Forces
34(1)
1.9.4 Newton's Laws
35(1)
a Rectilinear Motion
35(1)
b Rotational Motion
36(1)
1.9.5 Kinetic Energy
36(1)
1.9.6 Conservation of Linear and Angular Momentum
36(1)
a Rectilinear Motion
37(1)
b Rotational Motion
37(1)
1.9.7 D'Alembert's Principle
37(1)
1.9.8 Extension of Principles to System of Particles and Deformable Bodies
38(1)
1.9.9 Conservation of Momentum versus Conservation of Energy
38(1)
1.9.10 Instability of Rigid Body Spinning Freely in Space
39(1)
1.10 Elements of Analytical Mechanics
39(16)
1.10.1 Generalized Coordinates and Its Derivatives
40(2)
1.10.2 Lagrange's Equations
42(13)
a Elastic Forces
42(1)
b Damping Forces
43(1)
c External Loads
44(1)
d Inertia Forces
45(1)
e Combined Virtual Work
45(10)
2 Single Degree of Freedom Systems 55(76)
2.1 The Damped SDOF Oscillator
55(12)
2.1.1 Free Vibration: Homogeneous Solution
56(3)
Underdamped Case (xi < 1)
57(1)
Critically Damped Case (xi = 1)
58(1)
Overdamped Case (xi > 1)
59(1)
2.1.2 Response Parameters
59(1)
2.1.3 Homogeneous Solution via Complex Frequencies: System Poles
60(1)
2.1.4 Free Vibration of an SDOF System with Time-Varying Mass
61(2)
2.1.5 Free Vibration of SDOF System with Frictional Damping
63(4)
a System Subjected to Initial Displacement
64(1)
b Arbitrary Initial Conditions
65(2)
2.2 Phase Portrait: Another Way to View Systems
67(6)
2.2.1 Preliminaries
67(2)
2.2.2 Fundamental Properties of Phase Lines
69(2)
Trajectory Arrows
69(1)
Intersection of Phase Lines with Horizontal Axis
70(1)
Asymptotic Behavior at Singular Points and Separatrix
70(1)
Period of Oscillation
71(1)
2.2.3 Examples of Application
71(2)
Phase Lines of a Linear SDOF System
71(1)
Ball Rolling on a Smooth Slope
71(2)
2.3 Measures of Damping
73(3)
2.3.1 Logarithmic Decrement
74(1)
2.3.2 Number of Cycles to 50% Amplitude
75(1)
2.3.3 Other Forms of Damping
76(1)
2.4 Forced Vibrations
76(9)
2.4.1 Forced Vibrations: Particular Solution
76(3)
a Heuristic Method
77(1)
b Variation of Parameters Method
78(1)
2.4.2 Forced Vibrations: General Solution
79(1)
2.4.3 Step Load of Infinite Duration
80(1)
2.4.4 Step Load of Finite Duration (Rectangular Load, or Box Load)
81(1)
2.4.5 Impulse Response Function
81(2)
2.4.6 Arbitrary Forcing Function: Convolution
83(2)
Convolution Integral
83(1)
Time Derivatives of the Convolution Integral
84(1)
Convolution as a Particular Solution
84(1)
2.5 Support Motion in SDOF Systems
85(7)
2.5.1 General Considerations
85(3)
2.5.2 Response Spectrum
88(1)
Tripartite Spectrum
88(1)
2.5.3 Ship on Rough Seas, or Car on Bumpy Road
89(3)
2.6 Harmonic Excitation: Steady-State Response
92(14)
2.6.1 Transfer Function Due to Harmonic Force
92(4)
2.6.2 Transfer Function Due to Harmonic Support Motion
96(4)
2.6.3 Eccentric Mass Vibrator
100(2)
Experimental Observation
101(1)
2.6.4 Response to Suddenly Applied Sinusoidal Load
102(1)
2.6.5 Half-Power Bandwidth Method
103(3)
Application of Half-Power Bandwidth Method
105(1)
2.7 Response to Periodic Loading
106(9)
2.7.1 Periodic Load Cast in Terms of Fourier Series
106(1)
2.7.2 Nonperiodic Load as Limit of Load with Infinite Period
107(2)
2.7.3 System Subjected to Periodic Loading: Solution in the Time Domain
109(2)
2.7.4 Transfer Function versus Impulse Response Function
111(1)
2.7.5 Fourier Inversion of Transfer Function by Contour Integration
111(3)
Location of Poles, Fourier Transforms, and Causality
113(1)
2.7.6 Response Computation in the Frequency Domain
114(1)
1 Trailing Zeros
115(1)
2 Exponential Window Method: The Preferred Strategy
115(1)
2.8 Dynamic Stiffness or Impedance
115(3)
2.8.1 Connection of Impedances in Series and/or Parallel
117(1)
Standard Solid
118(1)
2.9 Energy Dissipation through Damping
118(13)
2.9.1 Viscous Damping
119(4)
Instantaneous Power and Power Dissipation
119(1)
Human Power
120(1)
Average Power Dissipated in Harmonic Support Motion
120(1)
Ratio of Energy Dissipated to Energy Stored
121(1)
Hysteresis Loop for Spring-Dashpot System
122(1)
2.9.2 Hysteretic Damping
123(1)
Ratio of Energy Dissipated to Energy Stored
123(1)
Instantaneous Power and Power Dissipation via the Hilbert Transform
124(1)
2.9.3 Power Dissipation during Broadband Base Excitation
124(1)
2.9.4 Comparing the Transfer Functions for Viscous and Hysteretic Damping
125(2)
Best Match between Viscous and Hysteretic Oscillator
126(1)
2.9.5 Locus of Viscous and Hysteretic Transfer Function
127(4)
3 Multiple Degree of Freedom Systems 131(120)
3.1 Multidegree of Freedom Systems
131(10)
3.1.1 Free Vibration Modes of Undamped MDOF Systems Orthogonality Conditions
132(2)
Normalized Eigenvectors
134(1)
3.1.2 Expansion Theorem
134(3)
3.1.3 Free Vibration of Undamped System Subjected to Initial Conditions
137(1)
3.1.4 Modal Partition of Energy in an Undamped MDOF System
137(1)
3.1.5 What If the Stiffness and Mass Matrices Are Not Symmetric?
138(1)
3.1.6 Physically Homogeneous Variables and Dimensionless Coordinates
139(2)
3.2 Effect of Static Loads on Structural Frequencies: H-is Effects
141(5)
3.2.1 Effective Lateral Stiffness
141(3)
3.2.2 Vibration of Cantilever Column under Gravity Loads
144(1)
3.2.3 Buckling of Column with Rotations Prevented
145(1)
3.2.4 Vibration of Cantilever Shear Beam
146(1)
3.3 Estimation of Frequencies
146(16)
3.3.1 Rayleigh Quotient
147(2)
Rayleigh-Schwarz Quotients
149(1)
3.3.2 Dunkerley-Mikhlin Method
149(8)
Dunkerley's Method for Systems with Rigid-Body Modes
154(3)
3.3.3 Effect on Frequencies of a Perturbation in the Structural Properties
157(5)
Perturbation of Mass Matrix
158(1)
Perturbation of Stiffness Matrix
159(1)
Qualitative Implications of Perturbation Formulas
160(2)
3.4 Spacing Properties of Natural Frequencies
162(14)
3.4.1 The Minimax Property of Rayleigh's Quotient
162(3)
3.4.2 Interlacing of Eigenvalues for Systems with Single External Constraint
165(2)
Single Elastic External Support
166(1)
3.4.3 Interlacing of Eigenvalues for Systems with Single Internal Constraint
167(1)
Single Elastic Internal Constraint
167(1)
3.4.4 Number of Eigenvalues in Some Frequency Interval
167(9)
Sturm Sequence Property
167(1)
The Sign Count of the Shifted Stiffness Matrix
168(2)
Root Count for Dynamically Condensed Systems
170(3)
Generalization to Continuous Systems
173(3)
3.5 Vibrations of Damped MDOF Systems
176(20)
3.5.1 Vibrations of Proportionally Damped MDOF Systems
176(5)
3.5.2 Proportional versus Nonproportional Damping Matrices
181(1)
3.5.3 Conditions under Which a Damping Matrix Is Proportional
181(2)
3.5.4 Bounds to Coupling Terms in Modal Transformation
183(1)
3.5.5 Rayleigh Damping
184(1)
3.5.6 Caughey Damping
185(4)
3.5.7 Damping Matrix Satisfying Prescribed Modal Damping Ratios
189(2)
3.5.8 Construction of Nonproportional Damping Matrices
191(3)
3.5.9 Weighted Modal Damping: The Biggs-Roesset Equation
194(2)
3.6 Support Motions in MDOF Systems
196(13)
3.6.1 Structure with Single Translational DOF at Each Mass Point
197(3)
Solution by Modal Superposition (Proportional Damping)
198(2)
3.6.2 MDOF System Subjected to Multicomponent Support Motion
200(3)
3.6.3 Number of Modes in Modal Summation
203(2)
3.6.4 Static Correction
205(2)
3.6.5 Structures Subjected to Spatially Varying Support Motion
207(2)
3.7 Nonclassical, Complex Modes
209(14)
3.7.1 Quadratic Eigenvalue Problem
210(1)
3.7.2 Poles or Complex Frequencies
210(3)
3.7.3 Doubled-Up Form of Differential Equation
213(2)
3.7.4 Orthogonality Conditions
215(1)
3.7.5 Modal Superposition with Complex Modes
216(5)
3.7.6 Computation of Complex Modes
221(2)
3.8 Frequency Domain Analysis of MDOF Systems
223(15)
3.8.1 Steady-State Response of MDOF Systems to Structural Loads
223(1)
3.8.2 Steady-State Response of MDOF System Due to Support Motion
224(7)
3.8.3 In-Phase, Antiphase, and Opposite-Phase Motions
231(2)
3.8.4 Zeros of Transfer Functions at Point of Application of Load
233(1)
3.8.5 Steady-State Response of Structures with Hysteretic Damping
234(1)
3.8.6 Transient Response of MDOF Systems via Fourier Synthesis
235(1)
3.8.7 Decibel Scale
236(1)
3.8.8 Reciprocity Principle
236(2)
3.9 Harmonic Vibrations Due to Vortex Shedding
238(1)
3.10 Vibration Absorbers
239(12)
3.10.1 Tuned Mass Damper
239(4)
3.10.2 Lanchester Mass Damper
243(1)
3.10.3 Examples of Application of Vibration Absorbers
244(5)
3.10.4 Torsional Vibration Absorber
249(2)
4 Continuous Systems 251(82)
4.1 Mathematical Characteristics of Continuous Systems
251(9)
4.1.1 Taut String
251(1)
4.1.2 Rods and Bars
252(1)
4.1.3 Bending Beam, Rotational Inertia Neglected
252(2)
4.1.4 Bending Beam, Rotational Inertia Included
254(1)
4.1.5 Timoshenko Beam
254(2)
4.1.6 Plate Bending
256(1)
4.1.7 Vibrations in Solids
257(1)
4.1.8 General Mathematical Form of Continuous Systems
258(1)
4.1.9 Orthogonality of Modes in Continuous Systems
259(1)
4.2 Exact Solutions for Simple Continuous Systems
260(45)
4.2.1 Homogeneous Rod
260(7)
Normal Modes of a Finite Rod
262(1)
Fixed-Fixed Rod
262(1)
Free-Free Rod
263(1)
Fixed-Free Rod
264(1)
Normal Modes of a Rod without Solving a Differential Equation
264(1)
Orthogonality of Rod Modes
265(2)
4.2.2 Euler-Bernoulli Beam (Bending Beam)
267(7)
Normal Modes of a Finite-Length Euler-Bernoulli Beam
268(1)
Simply Supported Beam
269(1)
Other Boundary Conditions
269(1)
Normal Modes of a Free-Free Beam
270(3)
Normal Modes of a Cantilever Beam
273(1)
Orthogonality Conditions of a Bending Beam
274(1)
Strain and Kinetic Energies of a Beam
274(1)
4.2.3 Bending Beam Subjected to Moving Harmonic Load
274(3)
Homogeneous Solution
275(1)
Particular Solution
275(2)
4.2.4 Nonuniform Bending Beam
277(2)
4.2.5 Nonclassical Modes of Uniform Shear Beam
279(8)
Dynamic Equations of Shear Beam
280(1)
Modes of Rotationally Unrestrained Shear Beam
281(6)
Concluding Observations
287(1)
4.2.6 Inhomogeneous Shear Beam
287(5)
Solution for Shear Modulus Growing Unboundedly with Depth
288(1)
Finite Layer of Inhomogeneous Soil
289(1)
Special Case: Shear Modulus Zero at Free Surface
290(1)
Special Case: Linearly Increasing Shear Wave Velocity
291(1)
4.2.7 Rectangular Prism Subjected to SH Waves
292(3)
Normal Modes
292(1)
Forced Vibration
293(2)
4.2.8 Cones, Frustums, and Horns
295(7)
a Exponential Horn
296(3)
b Frustum Growing as a Power of the Axial Distance
299(2)
c Cones of Infinite Depth with Bounded Growth of Cross Section
301(1)
4.2.9 Simply Supported, Homogeneous, Rectangular Plate
302(3)
Orthogonality Conditions of General Plate
302(1)
Simply Supported, Homogeneous Rectangular Plate
303(2)
4.3 Continuous, Wave-Based Elements (Spectral Elements)
305(28)
4.3.1 Impedance of a Finite Rod
306(5)
4.3.2 Impedance of a Semi-infinite Rod
311(1)
4.3.3 Viscoelastic Rod on a Viscous Foundation (Damped Rod)
311(7)
Stress and Velocity
313(1)
Power Flow
314(4)
4.3.4 Impedance of a Euler Beam
318(4)
4.3.5 Impedance of a Semi-infinite Beam
322(1)
4.3.6 Infinite Euler Beam with Springs at Regular Intervals
323(5)
Cutoff Frequencies
326(1)
Static Roots
327(1)
4.3.7 Semi-infinite Euler Beam Subjected to Bending Combined with Tension
328(5)
Power Transmission
331(1)
Power Transmission after Evanescent Wave Has Decayed
331(2)
5 Wave Propagation 333(38)
5.1 Fundamentals of Wave Propagation
333(15)
5.1.1 Waves in Elastic Bodies
333(1)
5.1.2 Normal Modes and Dispersive Properties of Simple Systems
334(8)
An Infinite Rod
334(2)
Gravity Waves in a Deep Ocean
336(1)
An Infinite Bending Beam
337(1)
A Bending Beam on an Elastic Foundation
338(2)
A Bending Beam on an Elastic Half-Space
340(1)
Elastic Thick Plate (Mindlin Plate)
341(1)
5.1.3 Standing Waves, Wave Groups, Group Velocity, and Wave Dispersion
342(3)
Standing Waves
342(1)
Groups and Group Velocity
343(1)
Wave Groups and the Beating Phenomenon
344(1)
Summary of Concepts
344(1)
5.1.4 Impedance of an Infinite Rod
345(3)
5.2 Waves in Layered Media via Spectral Elements
348(23)
5.2.1 SH Waves and Generalized Love Waves
349(9)
A Normal Modes
353(2)
B Source Problem
355(1)
C Wave Amplification Problem
355(3)
5.2.2 SV-P Waves and Generalized Rayleigh Waves
358(4)
Normal Modes
362(1)
5.2.3 Stiffness Matrix Method in Cylindrical Coordinates
362(3)
5.2.4 Accurate Integration of Wavenumber Integrals
365(6)
Maximum Wavenumber for Truncation and Layer Coupling Static Asymptotic Behavior: Tail of Integrals
367(2)
Wavenumber Step
369(2)
6 Numerical Methods 371(110)
6.1 Normal Modes by Inverse Iteration
371(7)
6.1.1 Fundamental Mode
371(3)
6.1.2 Higher Modes: Gram-Schmidt Sweeping Technique
374(1)
6.1.3 Inverse Iteration with Shift by Rayleigh Quotient
374(2)
6.1.4 Improving Eigenvectors after Inverse Iteration
376(1)
6.1.5 Inverse Iteration for Continuous Systems
377(1)
6.2 Method of Weighted Residuals
378(6)
6.2.1 Point Collocation
381(1)
6.2.2 Sub-domain
381(1)
6.2.3 Least Squares
381(1)
6.2.4 Galerkin
381(3)
6.3 Rayleigh-Ritz Method
384(7)
6.3.1 Boundary Conditions and Continuity Requirements in Rayleigh-Ritz
385(1)
6.3.2 Rayleigh-Ritz versus Galerkin
386(1)
6.3.3 Rayleigh-Ritz versus Finite Elements
387(1)
6.3.4 Rayleigh-Ritz Method for Discrete Systems
388(2)
6.3.5 Trial Functions versus True Modes
390(1)
6.4 Discrete Systems via Lagrange's Equations
391(9)
6.4.1 Assumed Modes Method
391(1)
6.4.2 Partial Derivatives
391(1)
6.4.3 Examples of Application
392(7)
6.4.4 What If Some of the Discrete Equations Remain Uncoupled?
399(1)
6.5 Numerical Integration in the Time Domain
400(17)
6.5.1 Physical Approximations to the Forcing Function
401(2)
6.5.2 Physical Approximations to the Response
403(3)
Constant Acceleration Method
403(1)
Linear Acceleration Method
404(1)
Newmark's beta Method
404(1)
Impulse Acceleration Method
405(1)
6.5.3 Methods Based on Mathematical Approximations
406(4)
Multistep Methods for First-Order Differential Equations
407(2)
Difference and Integration Formulas
409(1)
Multistep Methods for Second-Order Differential Equations
409(1)
6.5.4 Runge-Kutta Type Methods
410(3)
Euler's Method
411(1)
Improved and Modified Euler Methods
411(1)
The Normal Runge-Kutta Method
412(1)
6.5.5 Stability and Convergence Conditions for Multistep Methods
413(3)
Conditional and Unconditional Stability of Linear Systems
413(3)
6.5.6 Stability Considerations for Implicit Integration Schemes
416(1)
6.6 Fundamentals of Fourier Methods
417(23)
6.6.1 Fourier Transform
417(3)
6.6.2 Fourier Series
420(2)
6.6.3 Discrete Fourier Transform
422(1)
6.6.4 Discrete Fourier Series
423(3)
6.6.5 The Fast Fourier Transform
426(1)
6.6.6 Orthogonality Properties of Fourier Expansions
427(1)
a Fourier Transform
427(1)
b Fourier Series
427(1)
c Discrete Fourier Series
427(1)
6.6.7 Fourier Series Representation of a Train of Periodic Impulses
428(1)
6.6.8 Wraparound, Folding, and Aliasing
428(2)
6.6.9 Trigonometric Interpolation and the Fundamental Sampling Theorem
430(2)
6.6.10 Smoothing, Filtering, Truncation, and Data Decimation
432(1)
6.6.11 Mean Value
432(1)
6.6.12 Parseval's Theorem
433(1)
6.6.13 Summary of Important Points
434(1)
6.6.14 Frequency Domain Analysis of Lightly Damped or Undamped Systems
434(6)
Exponential Window Method: The Preferred Tool
435(5)
6.7 Fundamentals of Finite Elements
440(41)
6.7.1 Gaussian Quadrature
441(3)
Normalization
442(2)
6.7.2 Integration in the Plane
444(7)
a Integral over a Rectangular Area
446(1)
b Integral over a Triangular Area
447(1)
c Curvilinear Triangle
448(2)
d Quadrilateral
450(1)
e Curvilinear Quadrilateral
451(1)
Inadmissible Shapes
451(1)
6.7.3 Finite Elements via Principle of Virtual Displacements
451(4)
a Consistency
454(1)
b Conformity
454(1)
c Rigid Body Test
454(1)
d Convergence (Patch Test)
454(1)
6.7.4 Plate Stretching Elements (Plane Strain)
455(4)
a Triangular Element
455(2)
b Rectangular Element
457(2)
6.7.5 Isoparametric Elements
459(22)
Plane Strain Curvilinear Quadrilaterals
459(4)
Cylindrical Coordinates
463(18)
7 Earthquake Engineering and Soil Dynamics 481(84)
7.1 Stochastic Processes in Soil Dynamics
481(13)
7.1.1 Expectations of a Random Process
481(1)
7.1.2 Functions of Random Variable
482(1)
7.1.3 Stationary Processes
482(1)
7.1.4 Ergodic Processes
483(1)
7.1.5 Spectral Density Functions
483(1)
7.1.6 Coherence Function
484(1)
7.1.7 Estimation of Spectral Properties
484(4)
7.1.8 Spatial Coherence of Seismic Motions
488(6)
Coherency Function Based on Statistical Analyses of Actual Earthquake Motions
488(2)
Wave Model for Random Field
490(1)
Simple Cross-Spectrum for SH Waves
490(3)
Stochastic Deconvolution
493(1)
7.2 Earthquakes, and Measures of Quake Strength
494(8)
7.2.1 Magnitude
495(2)
Seismic Moment
495(2)
Moment Magnitude
497(1)
7.2.2 Seismic Intensity
497(2)
7.2.3 Seismic Risk: Gutenberg-Richter Law
499(1)
7.2.4 Direction of Intense Shaking
500(2)
7.3 Ground Response Spectra
502(11)
7.3.1 Preliminary Concepts
502(2)
7.3.2 Tripartite Response Spectrum
504(1)
7.3.3 Design Spectra
505(1)
7.3.4 Design Spectrum in the style of ASCE/SEI-7-05
506(1)
Design Earthquake
506(1)
Transition Periods
506(1)
Implied Ground Motion Parameters
507(1)
7.3.5 MDOF Systems: Estimating Maximum Values from Response Spectra
507(6)
Common Error in Modal Combination
510(1)
General Case: Response Spectrum Estimation for Complete Seismic Environment
511(2)
7.4 Dynamic Soil-Structure Interaction
513(38)
7.4.1 General Considerations
513(2)
Seismic Excitation (Free-Field Problem)
514(1)
Kinematic Interaction
514(1)
Inertial Interaction
515(1)
7.4.2 Modeling Considerations
515(2)
Continuum Solutions versus Finite Elements
515(1)
Finite Element Discretization
515(1)
Boundary Conditions
516(1)
7.4.3 Solution Methods
517(5)
Direct Approach
517(1)
Superposition Theorem
518(1)
Three-Step Approach
519(1)
Approximate Stiffness Functions
520(2)
7.4.4 Direct Formulation of SSI Problems
522(4)
The Substructure Theorem
522(2)
SSI Equations for Structures with Rigid Foundation
524(2)
7.4.5 SSI via Modal Synthesis in the Frequency Domain
526(8)
Partial Modal Summation
529(2)
What If the Modes Occupy Only a Subspace?
531(2)
Member Forces
533(1)
7.4.6 The Free-Field Problem: Elements of 1-D Soil Amplification
534(6)
Effect of Location of Control Motion in 1-D Soil Amplification
537(3)
7.4.7 Kinematic Interaction of Rigid Foundations
540(11)
Iguchi's Approximation, General Case
541(3)
Iguchi Approximation for Cylindrical Foundations Subjected to SH Waves
544(1)
Geometric Properties
545(1)
Free-Field Motion Components at Arbitrary Point, Zero Azimuth
546(1)
Surface Integrals
546(2)
Volume Integrals
548(1)
Effective Motions
549(2)
7.5 Simple Models for Time-Varying, Inelastic Soil Behavior
551(10)
7.5.1 Inelastic Material Subjected to Cyclic Loads
551(2)
7.5.2 Masing's Rule
553(2)
7.5.3 Ivan's Model: Set of Elastoplastic Springs in Parallel
555(1)
7.5.4 Hyperbolic Model
556(2)
7.5.5 Ramberg-Osgood Model
558(3)
7.6 Response of Soil Deposits to Blast Loads
561(4)
7.6.1 Effects of Ground-Borne Blast Vibrations on Structures
561(4)
Frequency Effects
561(1)
Distance Effects
562(1)
Structural Damage
563(2)
8 Advanced Topics 565(54)
8.1 The Hilbert Transform
565(8)
8.1.1 Definition
565(1)
8.1.2 Fourier Transform of the Sign Function
566(1)
8.1.3 Properties of the Hilbert Transform
567(2)
8.1.4 Causal Functions
569(1)
8.1.5 Kramers-Kronig Dispersion Relations
570(3)
Minimum Phase Systems
572(1)
Time-Shifted Causality
573(1)
8.2 Transfer Functions, Normal Modes, and Residues
573(7)
8.2.1 Poles and Zeros
573(1)
8.2.2 Special Case: No Damping
574(1)
8.2.3 Amplitude and Phase of the Transfer Function
575(5)
8.2.4 Normal Modes versus Residues
8.3 Correspondence Principle
580(2)
8.4 Numerical Correspondence of Damped and Undamped Solutions
582(3)
8.4.1 Numerical Quadrature Method
582(2)
8.4.2 Perturbation Method
584(1)
8.5 Gyroscopic Forces Due to Rotor Support Motions
585(5)
8.6 Rotationally Periodic Structures
590(6)
8.6.1 Structures Composed of Identical Units and with Polar Symmetry
590(3)
8.6.2 Basic Properties of Block-Circulant Matrices
593(1)
8.6.3 Dynamics of Rotationally Periodic Structures
594(2)
8.7 Spatially Periodic Structures
596(14)
8.7.1 Method 1: Solution in Terms of Transfer Matrices
596(6)
8.7.2 Method 2: Solution via Static Condensation and Cloning
602(2)
Example: Waves in a Thick Solid Rod Subjected to Dynamic Source
603(1)
8.7.3 Method 3: Solution via Wave Propagation Modes
604(6)
Example 1: Set of Identical Masses Hanging from a Taut String
605(3)
Example 2: Infinite Chain of Viscoelastically Supported Masses and Spring-Dashpots
608(2)
8.8 The Discrete Shear Beam
610(9)
8.8.1 Continuous Shear Beam
611(1)
8.8.2 Discrete Shear Beam
611(8)
9 Mathematical Tools 619(28)
9.1 Dirac Delta and Related Singularity Functions
619(2)
9.1.1 Related Singularity Functions
620(6)
Doublet Function
620(1)
Dirac Delta Function
620(1)
Unit Step Function (Heaviside Function)
620(1)
Unit Ramp Function
621(1)
9.2 Functions of Complex Variables: A Brief Summary
621(5)
9.3 Wavelets
626(4)
9.3.1 Box Function
626(1)
9.3.2 Hanning Bell (or Window)
626(1)
9.3.3 Gaussian Bell
627(1)
9.3.4 Modulated Sine Pulse (Antisymmetric Bell)
628(1)
9.3.5 Ricker Wavelet
628(2)
9.4 Useful Integrals Involving Exponentials
630(1)
9.4.1 Special Cases
630(1)
9.5 Integration Theorems in Two and Three Dimensions
630(3)
9.5.1 Integration by Parts
631(1)
9.5.2 Integration Theorems
631(2)
9.5.3 Particular Cases: Gauss, Stokes, and Green
633(1)
9.6 Positive Definiteness of Arbitrary Square Matrix
633(7)
9.7 Derivative of Matrix Determinant: The Trace Theorem
640(2)
9.8 Circulant and Block-Circulant Matrices
642(5)
9.8.1 Circulant Matrices
642(2)
9.8.2 Block-Circulant Matrices
644(3)
10 Problem Sets 647(66)
Author Index 713(1)
Subject Index 714
Professor Eduardo Kausel is a specialist in structural dynamics in the Department of Civil and Environmental Engineering at the Massachusetts Institute of Technology (MIT). He is especially well known for two papers on the collapse of the Twin Towers on September 11, 2001. The first of this pair, published on MIT's website only a few days after the terrorist act, attracted more readers around the world than all other works and publications on the subject combined. Kausel is the author of Fundamental Solutions in Elastodynamics: A Compendium (Cambridge, 2011).
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