CHAPTER 1: INTRODUCTION
1.1 Examples of Problems Related to Structural Dynamics
1.1.1 Tacoma Narrows bridge 1
1.1.2 A Hospital Building Subjected to an Earthquake
1.1.3 Wenchuan Earthquake (), China
1.1.4 Yogyakarta Earthquake
1.1.5 Kobe Earthquake
1.1.6 The Chi-Chi Earthquake (Taiwan)
1.2 Tower structures

CHAPTER 2: FORMULATION OF A MATHEMATICAL MODEL OF A SINGLE DEGREE OF FREEDOM SYSTEM
2.1 Idealized Structural System
2.2 Equation of Motion
2.2.1 Equation of Motion of One-Story Building Subjected to Dynamic Force
2.2.1.1 Problem Statement of One-Story Building Subjected to Dynamic Force
2.2.2 Equation of Motion of One-Story Building Subjected to Earthquake
2.2.2.1 Accelerograph Systems
2.2.2.2 Ground Acceleration Recordings
2.3 Multi Degree of Freedom Structures
2.4 Solution of Equation of Motion
2.5 Types of Dynamic Loading on Structures

CHAPTER 3: FREE VIBRATION RESPONSE OF SDF SYSTEMS
3.1 Equation of Motion of One-Story Building
3.2 Free Vibration Response of SDF Systems
3.3 A Quick Review of Basic Mathematical Concepts
3.3.1 Undamped Free Vibration Response
3.3.2 Damped Free Vibration Response
3.3.2.1 Case 2 (b) Underdamped Systems (c < 2m) 3.3.2.2 Case 2 (c) Critical Damped Systems (c = cc = 2m) 3.3.2.3 Case 2 (a) Overdamped Systems (c > cc = 2m)
3.3.2.4 Summary of Free Damped Systems
3.3.2.5 Free Vibration Tests

CHAPTER 4: RESPONSE OF SDF SYSTEMS TO HARMONIC LOADING
4.1 Harmonic Forces
4.2 Response to Harmonic Forces
4.3 A Quick Review of Basic Mathematical Concepts
4.4 Response of Undamped SDF Systems to Harmonic Loading
4.5 Response of Damped SDF Systems to Harmonic Loading
4.6 Response of Damped SDF Systems to Harmonic Ground Motions

CHAPTER 5: RESPONSE OF SDF SYSTEMS TO PERIODIC LOADING
5.1 Periodic Loading
5.2 Fourier Series Representation of a Periodic Function
5.2.1 Fourier Decomposition
5.2.2 Fourier Series
5.2.3 Fourier Series Example
5.2.4 Response to a Periodic Loading
5.2.4.1 Steady-State Response to a Periodic Loading
5.3 Example

CHAPTER 6: RESPONSE OF SDF SYSTEMS TO IMPULSE LOADING
6.1 Impulse Loading
6.2 Response to Impulse Loading

CHAPTER 7: RESPONSE OF SDF SYSTEMS TO GENERAL DYNAMIC LOADING
7.1 Duhamel’s Integral
7.2 Response to General Dynamic Loading – Duhamel’s Integral
7.3 Numerical Integration
7.3.1 Solving Duhamel’s Integral using Numerical Integration
7.3.2 Numerical Example
7.3.3 Application
7.4 Step-by-Step Direct Integration Method or Time-Stepping Method
7.4.1 Step-by-Step Direct Integration Procedure
7.4.2 Additional Notes to Step-by-Step Direct Integration Procedure
7.4.3 Numerical Example of Step-by-Step Direct Integration Procedure

CHAPTER 8: EARTHQUAKE RESPONSE OF SDF SYSTEMS – CONCEPT OF ELASTIC RESPONSE SPECTRUM THE CONCEPT OF RESPONSE SPECTRUM
8.1 Pseudo-Velocity Response Spectrum
8.2 Pseudo-Acceleration Response Spectrum
8.3 Combined D-V-A Response Spectrum
8.4 Construction of Response Spectrum
8.5 Solved Example

CHAPTER 9: DYNAMICS OF SIMPLE STRUCTURES – A SUMMARY
CHAPTER 10: EARTHQUAKE RESPONSE OF INELASTIC SDF SYSTEMS
(CONCEPT OF INELASTIC RESPONSE SPECTRUM AND DESIGN SPECTRUM)
10.1 The Concept of Elastic Design Spectrum
10.1.1 Elastic Design Spectra
10.1.2 Construction of Elastic Design Spectra
10.1.3 Modern Methods for the Construction of Elastic Design Spectra
10.1.4 The Use of Elastic Design Spectra
10.1.5 Comparison of Elastic Design RS and Actual RS
10.1.6 Distinction between Elastic Design R.S. and Actual R.S.
10.1.7 Design Response Spectrum (UBC )
10.2 The Concept of Inelastic Response Spectrum
10.3 The Earthquake Response of Inelastic SDF Systems
10.3.1 Force-Deformation Relationships
10.3.2 Force-Deformation Relation of a Reinforced Concrete Structure
10.3.3 Force-Deformation Relation of a Masonry Structure
10.3.4 Elastoplastic Idealization
10.4 Response of Elastoplastic System to Earthquake Ground Motion
10.5 Effects of Inelasticity on Earthquake Response
10.6 Constant-Ductility Spectrum
10.7 Design Options
10.8 Inelastic Design Response Spectra
10.9 The Concept of Overstrength and Ductility
10.10 The Basic Concept of R and Ω Factor in Building Codes
10.11 Response Reduction Factor
10.12 Deflection Amplification Factor
10.13 Overstrength Factor (Ωo)

CHAPTER 11: CONCEPT OF GENERALIZED SDF SYSTEMS
11.1 Generalized SDOF Systems
11.2 Systems with Distributed Mass and Elasticity Subjected to Ground Motions
11.2.1 Equation of Motion
11.2.2 Natural Vibration Frequency
11.2.3 Example.2-1
11.2.4 Example.2-2
11.3 Systems with Many Lumped Masses and Stiffness (Shear Building) Subjected to Ground Motions
11.3.1 Assumed Shape Vector
11.3.2 Example.3-1
11.3.3 Example.3-2

CHAPTER 12: FORMULATION OF MATHEMATICAL MODEL OF MDF SYSTEMS
12.1 Simplest Idealization of a Multi-story Building
12.2 Formulation of Equations of Motion by Direct Dynamic Equilibrium
Approach
12.3 Simplest Idealization of a Multi-story Building
12.4 Formulation of Equations of Motion
12.5 Formulation of Equations of Motion by Variational Approach
(or Energy Approach)
12.6 Kinetic Energy (T)
12.7 Potential Energy (U)
12.8 Strain Energy in Linear Spring
12.9 Strain Energy on Element on Volume under Uni-axial Stress State
12.10 Strain Energy in an Axially Loaded Prismatic Bar
12.11 Bending Strain Energy in Beam
12.12 Gravity Potential
12.13 Generalized Coordinates: Discrete Structures
12.14 Generalized Coordinates: Continuous Structures
12.15 Example: Transverse Vibration of a Simple Beam
12.16 Variational Principle: A Review
12.17 Hamilton’s Principle
12.18 Lagrange’s Equations of Motion
12.19 Example 1: A 3-Story Building
12.20 Example 2: Transverse Vibration of a Uniform Beam

CHAPTER 13: MODAL ANALYSIS FOR FREE VIBRATION RESPONSE OF MDF SYSTEMS
13.1 Undamped Free Vibration of Multi-Degree-of-Freedom Structures
13.2 Example: Natural Frequencies and Mode Shapes of a 3-story Shear Building
13.3 Undamped Free Vibration of Multi-degree-of-freedom Structures
13.4 Orthogonality Conditions
13.5 Finite Element Concept in Dynamics
13.6 Finite Element Approach: Example
13.7 Properties of Mass, Stiffness and Damping Matrices

CHAPTER 14: MODAL ANALYSIS FOR FORCED VIBRATION RESPONSE OF MDF SYSTEMS
14.1 Concept of Generalized Coordinates
14.2 Equations of Motion in Normal Coordinates Uncoupled Equations
14.3 Example: Forced Vibration Response of a Uniform Cantilever Beam
14.4 Additional Notes on the Modal Analysis Method

CHAPTER 15: DAMPING IN DYNAMIC ANALYSIS OF STRUCTURES
15.1 Damping Mechanisms and Models
15.2 Role of Damping in Vibrations
15.3 Mechanisms of Damping
15.4 Linear Models of Damping
15.5 Role of Damping in Dynamic Response of MDF Systems
15.6 Formulation of Damping Matrix by Modal Damping Approach

CHAPTER 16: NUMERICAL EVALUATION OF DYNAMIC RESPONSE – STEP-BYSTEP DIRECT INTEGRATION – MDF SYSTEMS
16.1 Step-by-Step Direct Integration
16.2 Incremental Equilibrium Equations
16.3 Numerical Damping & Period Elongation
The effect of error accumulation
16.4 Wilson-θ Method
16.5 Performance of Wilson-θ Method

CHAPTER 17: DYNAMICS OF CONTINUOUS STRUCTURES
17.1 Continuous Structures Partial Differential Equations of Motion
17.2 Transverse Vibration of String
17.3 Transverse Vibration of Beam
17.4 Axial Vibration of Rod
17.5 Orthogonality of Mode Shapes
17.6 Forced Vibration Modal Analysis
17.7 Example of Modal Analysis

CHAPTER 18: RANDOM VIBRATION
18.1 Introduction
18.2 Probability Theory
18.3 Response of a SDOF System to Stationary Random Force
18.4 Numerical Example