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Preface to Structural Dynamics—An Introduction to Computer Methods
Preface to Fundamentals of Structural Dynamics
About the Authors
Chapter 1: The Science and Art of Structural Dynamics
1.1 INTRODUCTION TO STRUCTURAL DYNAMICS
1.2 MODELING OF STRUCTURAL COMPONENTS AND SYSTEMS
1.3 PROTOTYPE SPRING–MASS MODEL
1.4 VIBRATION TESTING OF STRUCTURES
1.5 SCOPE OF THE BOOK
1.6 COMPUTER SIMULATIONS; SUPPLEMENTARY MATERIAL ON THE WEBSITE
Part I Single-Degree-of-Freedom Systems
Chapter 2: Mathematical Models of SDOF Systems
2.1 BRIEF REVIEW OF THE DYNAMICS OF PARTICLES AND RIGID BODIES
2.2 ELEMENTS OF LUMPED-PARAMETER MODELS
2.3 APPLICATION OF NEWTON'S LAWS TO LUMPED-PARAMETER MODELS
2.4 APPLICATION OF THE PRINCIPLE OF VIRTUAL DISPLACEMENTS TO LUMPED-PARAMETER MODELS
2.5 APPLICATION OF THE PRINCIPLE OF VIRTUAL DISPLACEMENTS TO CONTINUOUS MODELS: ASSUMED-MODES METHOD
Chapter 3: Free Vibration of SDOF Systems
3.1 FREE VIBRATION OF UNDAMPED SDOF SYSTEMS
3.2 FREE VIBRATION OF VISCOUS-DAMPED SDOF SYSTEMS
3.3 STABILITY OF MOTION
3.4 FREE VIBRATION OF AN SDOF SYSTEM WITH COULOMB DAMPING
3.5 EXPERIMENTAL DETERMINATION OF THE NATURAL FREQUENCY AND DAMPING FACTOR OF AN SDOF SYSTEM
Chapter 4: Response of SDOF Systems to Harmonic Excitation
4.1 RESPONSE OF UNDAMPED SDOF SYSTEMS TO HARMONIC EXCITATION
4.2 RESPONSE OF VISCOUS-DAMPED SDOF SYSTEMS TO HARMONIC EXCITATION: FREQUENCY-RESPONSE FUNCTIONS
4.3 COMPLEX FREQUENCY RESPONSE
4.4 VIBRATION ISOLATION: FORCE TRANSMISSIBILITY AND BASE MOTION
4.5 VIBRATION MEASURING INSTRUMENTS: ACCELEROMETERS AND VIBROMETERS
4.6 USE OF FREQUENCY-RESPONSE DATA TO DETERMINE THE NATURAL FREQUENCY AND DAMPING FACTOR OF A LIGHTLY DAMPED SDOF SYSTEM
4.7 EQUIVALENT VISCOUS DAMPING
4.8 STRUCTURAL DAMPING
Chapter 5: Response of SDOF Systems to Nonperiodic Excitation
5.1 RESPONSE OF A VISCOUS-DAMPED SDOF SYSTEM TO AN IDEAL STEP INPUT
5.2 RESPONSE OF UNDAMPED SDOF SYSTEMS TO RECTANGULAR PULSE AND RAMP LOADINGS
5.3 RESPONSE OF UNDAMPED SDOF SYSTEMS TO A SHORT-DURATION IMPULSE: UNIT IMPULSE RESPONSE
5.4 RESPONSE OF SDOF SYSTEMS TO GENERAL DYNAMIC EXCITATION: CONVOLUTION INTEGRAL METHOD
5.5 RESPONSE SPECTRA
5.6 SYSTEM RESPONSE BY THE LAPLACE TRANSFORM METHOD: SYSTEM TRANSFER FUNCTION
Chapter 6 Numerical Evaluation of the Dynamic Response of SDOF Systems
6.1 INTEGRATION OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS
6.2 INTEGRATION OF FIRST-ORDER ORDINARY DIFFERENTIAL EQUATION
6.3 NONLINEAR SDOF SYSTEMS
Chapter 7: Response of SDOF Systems to Periodic Excitation: Frequency-Domain Analysis
7.1 RESPONSE TO PERIODIC EXCITATION: REAL FOURIER SERIES
7.2 RESPONSE TO PERIODIC EXCITATION: COMPLEX FOURIER SERIES
7.3 RESPONSE TO NONPERIODIC EXCITATION: FOURIER INTEGRAL
7.4 RELATIONSHIP BETWEEN COMPLEX FREQUENCY RESPONSE AND UNIT IMPULSE RESPONSE
7.5 DISCRETE FOURIER TRANSFORM AND FAST FOURIER TRANSFORM
Part II Multiple-Degree-of-Freedom Systems—Basic Topics
Chapter 8: Mathematical Models of MDOF Systems
8.1 APPLICATION OF NEWTON'S LAWS TO LUMPED-PARAMETER MODELS
8.2 INTRODUCTION TO ANALYTICAL DYNAMICS: HAMILTON'S PRINCIPLE AND LAGRANGE'S EQUATIONS
8.3 APPLICATION OF LAGRANGE'S EQUATIONS TO LUMPED-PARAMETER MODELS
8.4 APPLICATION OF LAGRANGE'S EQUATIONS TO CONTINUOUS MODELS: ASSUMED-MODES METHOD
8.5 CONSTRAINED COORDINATES AND LAGRANGE MULTIPLIERS
Chapter 9 Vibration of Undamped 2-DOF Systems
9.1 FREE VIBRATION OF 2-DOF SYSTEMS: NATURAL FREQUENCIES AND MODE SHAPES
9.2 BEAT PHENOMENON
9.3 ADDITIONAL EXAMPLES OF MODES AND FREQUENCIES OF 2-DOF SYSTEMS: ASSUMED-MODES MODELS
9.4 FREE VIBRATION OF SYSTEMS WITH RIGID-BODY MODES
9.5 INTRODUCTION TO MODE SUPERPOSITION: FREQUENCY RESPONSE OF AN UNDAMPED 2-DOF SYSTEM
9.6 UNDAMPED VIBRATION ABSORBER
Chapter 10: Vibration Properties of MDOF Systems: Modes, Frequencies, and Damping
10.1 SOME PROPERTIES OF NATURAL FREQUENCIES AND NATURAL MODES OF UNDAMPED MDOF SYSTEMS
10.2 MODEL REDUCTION: RAYLEIGH, RAYLEIGH–RITZ, AND ASSUMED-MODES METHODS
10.3 UNCOUPLED DAMPING IN MDOF SYSTEMS
10.4 STRUCTURES WITH ARBITRARY VISCOUS DAMPING: COMPLEX MODES
10.5 NATURAL FREQUENCIES AND MODE SHAPES OF DAMPED STRUCTURES WITH RIGID-BODY MODES
Chapter 11: Dynamic Response of MDOF Systems: Mode-Superposition Method
11.1 MODE-SUPERPOSITION METHOD: PRINCIPAL COORDINATES
11.2 MODE-SUPERPOSITION SOLUTIONS FOR MDOF SYSTEMS WITH MODAL DAMPING: FREQUENCY-RESPONSE ANALYSIS
11.3 MODE-DISPLACEMENT SOLUTION FOR THE RESPONSE OF MDOF SYSTEMS
11.4 MODE-ACCELERATION SOLUTION FOR THE RESPONSE OF UNDAMPED MDOF SYSTEMS
11.5 DYNAMIC STRESSES BY MODE SUPERPOSITION
11.6 MODE SUPERPOSITION FOR UNDAMPED SYSTEMS WITH RIGID-BODY MODES
Part III Continuous Systems
Chapter 12: Mathematical Models of Continuous Systems
12.1 APPLICATIONS OF NEWTON'S LAWS: AXIAL DEFORMATION AND TORSION
12.2 APPLICATION OF NEWTON'S LAWS: TRANSVERSE VIBRATION OF LINEARLY ELASTIC BEAMS (BERNOULLI–EULER BEAM THEORY)
12.3 APPLICATION OF HAMILTON'S PRINCIPLE: TORSION OF A ROD WITH CIRCULAR CROSS SECTION
12.4 APPLICATION OF THE EXTENDED HAMILTON'S PRINCIPLE: BEAM FLEXURE INCLUDING SHEAR DEFORMATION AND ROTATORY INERTIA (TIMOSHENKO BEAM THEORY)
Chapter 13: Free Vibration of Continuous Systems
13.1 FREE AXIAL AND TORSIONAL VIBRATION
13.2 FREE TRANSVERSE VIBRATION OF BERNOULLI–EULER BEAMS
13.3 RAYLEIGH'S METHOD FOR APPROXIMATING THE FUNDAMENTAL FREQUENCY OF A CONTINUOUS SYSTEM
13.4 FREE TRANSVERSE VIBRATION OF BEAMS INCLUDING SHEAR DEFORMATION AND ROTATORY INERTIA
13.5 SOME PROPERTIES OF NATURAL MODES OF CONTINUOUS SYSTEMS
13.6 FREE VIBRATION OF THIN FLAT PLATES
PART IV Computational Methods in Structural Dynamics
Chapter 14: Introduction to Finite Element Modeling of Structures
14.1 INTRODUCTION TO THE FINITE ELEMENT METHOD
14.2 ELEMENT STIFFNESS AND MASS MATRICES AND ELEMENT FORCE VECTOR
14.3 TRANSFORMATION OF ELEMENT MATRICES
14.4 ASSEMBLY OF SYSTEM MATRICES: DIRECT STIFFNESS METHOD
14.5 BOUNDARY CONDITIONS
14.6 CONSTRAINTS: REDUCTION OF DEGREES OF FREEDOM
14.7 SYSTEMS WITH RIGID-BODY MODES
14.8 FINITE ELEMENT SOLUTIONS FOR NATURAL FREQUENCIES AND MODE SHAPES
Chapter 15: Numerical Evaluation of Modes and Frequencies of MDOF Systems
15.1 INTRODUCTION TO METHODS FOR SOLVING ALGEBRAIC EIGENPROBLEMS
15.2 VECTOR ITERATION METHODS
15.3 SUBSPACE ITERATION
15.4 QR METHOD FOR SYMMETRIC EIGENPROBLEMS
15.5 LANCZOS EIGENSOLVER
15.6 NUMERICAL CASE STUDY
Chapter 16: Direct Integration Methods for Dynamic Response of MDOF Systems
16.1 DAMPING IN MDOF SYSTEMS
16.2 NUMERICAL INTEGRATION: MATHEMATICAL FRAMEWORK
16.3 INTEGRATION OF SECOND-ORDER MDOF SYSTEMS
16.4 SINGLE-STEP METHODS AND SPECTRAL STABILITY
16.5 NUMERICAL CASE STUDY
Chapter 17: Component-Mode Synthesis
17.1 INTRODUCTION TO COMPONENT-MODE SYNTHESIS
17.2 COMPONENT MODES: NORMAL, CONSTRAINT, AND RIGID-BODY MODES
17.3 COMPONENT MODES: ATTACHMENT AND INERTIA-RELIEF ATTACHMENT MODES
17.4 FLEXIBILITY MATRICES AND RESIDUAL FLEXIBILITY
17.5 SUBSTRUCTURE COUPLING PROCEDURES
17.6 COMPONENT-MODE SYNTHESIS METHODS: FIXED-INTERFACE METHODS
17.7 COMPONENT-MODE SYNTHESIS METHODS: FREE-INTERFACE METHODS
17.8 BRIEF INTRODUCTION TO MULTILEVEL SUBSTRUCTURING
PART V Advanced Topics in Structural Dynamics
Chapter 18: Introduction to Experimental Modal Analysis
18.1 INTRODUCTION
18.2 FREQUENCY-RESPONSE FUNCTION REPRESENTATIONS
18.3 VIBRATION TEST HARDWARE
18.4 FOURIER TRANSFORMS, DIGITAL SIGNAL PROCESSING, AND ESTIMATION OF FRFs
18.5 MODAL PARAMETER ESTIMATION
18.6 MODE SHAPE ESTIMATION AND MODEL VERIFICATION
Chapter 19: Introduction to Active Structures
19.1 INTRODUCTION TO PIEZOELECTRIC MATERIALS
19.2 CONSTITUTIVE LAWS OF LINEAR PIEZOELECTRICITY
19.3 APPLICATION OF NEWTON'S LAWS TO PIEZOSTRUCTURAL SYSTEMS
19.4 APPLICATION OF EXTENDED HAMILTON'S PRINCIPLE TO PIEZOELECTRICITY
19.5 ACTIVE TRUSS MODELS
19.6 ACTIVE BEAM MODELS
19.7 ACTIVE COMPOSITE LAMINATES
Chapter 20: Introduction to Earthquake Response of Structures
20.1 INTRODUCTION
20.2 RESPONSE OF A SDOF SYSTEM TO EARTHQUAKE EXCITATION: RESPONSE SPECTRA
20.3 RESPONSE OF MDOF SYSTEMS TO EARTHQUAKE EXCITATION
20.4 FURTHER CONSIDERATIONS
Appendix A: Units
Appendix B: Complex Numbers
Appendix C: Elements of Laplace Transforms
Appendix D: Fundamentals of Linear Algebra
Appendix E: Introduction to the Use of Matlab
Index
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