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Table of Contents

1. Basic Concepts.

Introduction to Structural Dynamics. Types of Dynamic Loads. Sources of Dynamic Loads. Distinguishing Features of a Dynamic Problem. Methodology for Dynamic Analysis. Types of Structural Vibration. Organization of the Text. Systems of Units. References.

I. SINGLE-DEGREE-OF-FREEDOM (SDOF) SYSTEMS.

2. Equation of Motion and Natural Frequency.

Fundamental Components of a Vibrating System. D’Alembert’s Principle of Dynamic Equilibrium. The Energy Method. The Principle of Virtual Displacements. References. Notation. Problems.

3. Undamped Free Vibration.

Simple Harmonic Motion. Interpretation of the Solution. Equivalent Stiffness. Rayleigh Method. References. Notation. Problems.

4. Damped Free Vibration.

Free Vibration with Viscous Damping. Logarithmic Decrement. Hysteresis Damping. Coulomb Damping. References. Notation. Problems.

5. Response to Harmonic Excitation.

Forced Harmonic Response of Undamped Systems. Beating and Resonance. Forced Harmonic Vibrations with Viscous Damping. Effect of Damping Factor on Steady-State Response and Phase Angle. Harmonic Excitation Caused by Rotating Unbalance. Base Excitation. Vibration Isolation and Transmissibility. References. Notation. Problems.

6. Response to Periodic and Arbitrary Dynamic Excitation.

Response to Periodic Excitation. Response to Unit Impulse. Duhamel Integral. Response to Arbitrary Dynamic Excitation. Response Spectrum. References. Notation. Problems.

7. Numerical Evaluation of Dynamic Response.

Interpolation of the Excitation. Direct Integration of the Equation of Motion. Central Difference Method. Runge-Kutta Methods. Average Acceleration Method. Linear Acceleration Method. Response to Base Excitation. Response Spectra by Numerical Integration. References. Notation. Problems.

8. Frequency Domain Analysis.

Alternative Forms of the Fourier Series. Discrete Fourier Transform. Fast Fourier Transform. Discrete Fourier Transform Implementation Considerations. Fourier Integral. References. Notation. Problems.

II. MULTI-DEGREE-OF-FREEDOM (MDOF) SYSTEMS.

9. General Property Matrices for Vibrating Systems.

Flexibility Matrix. Stiffness Matrix. Inertia Properties: Mass Matrix. The Eigenproblem in Vibration Analysis. Static Condensation of the Stiffness Matrix. References. Notation. Problems.

10. Equations of Motion and Undamped Free Vibration.

Hamilton’s Principle and the Lagrange Equations. Natural Vibration Frequencies. Natural Vibration Modes. Orthogonality of Natural Modes. Systems Admitting Rigid-Body Modes. Generalized Mass and Stiffness Matrices. Free Vibration Response to Initial Conditions. Approximate Methods for Estimating the Fundamental Frequency. References. Notation. Problems.

11. Numerical Solution Methods for Natural Frequencies and Mode Shapes.

General Solution Methods for Eigenproblems. Inverse Vector Iteration. Forward Vector Iteration. Generalized Jacobi Method. Solution Methods for Large Eigenproblems References. Notation. Problems.

12. Analysis of Dynamic Response by Mode Superposition.

Mode Displacement Method for Undamped Systems. Modal Participation Factor. Mode Superposition Solution for Systems with Classical Damping. Numerical Evaluation of Modal Response. Normal Mode Response to Support Motions. Response Spectrum Analysis. Mode Acceleration Method. References. Notation. Problems.

13. Analysis of Dynamic Response by Direct Integration.

Basic Concepts of Direct Integration Methods. The Central Difference Method. The Wilson-u Method. The Newmark Method. Practical Considerations for Damping. Stability and Accuracy of Direct Integration Methods. Direct Integration versus Mode Superposition. References. Notation. Problems.

III. CONTINUOUS SYSTEMS.

14. Vibrations of Continuous Systems.

Longitudinal Vibration of a Uniform Rod. Transverse Vibration of a Pretensioned CTable. Free Transverse Vibration of Uniform Beams. Orthogonality of Normal Modes. Undamped Forced Vibration of Beams by Mode Superposition. Approximate Methods. References. Notation. Problems.

IV. NONLINEAR DYNAMIC RESPONSE.

15. Analysis of Nonlinear Response.

Classification of Nonlinear Analyses. Systems with Nonlinear Characteristics. Formulation of Incremental Equations of Equilibrium. Numerical Solution of Nonlinear Equilibrium Equations. Response of Elastoplastic SDOF Systems. Response of Elastoplastic MDOF Systems. References. Notation. Problems.

V. PRACTICAL APPLICATIONS.

16. Elastic Wave Propagation in Solids.

Stress and Strain at a Point. Constitutive Relations. Equations of Motion. Stress Wave Propagation. Applications. References. Notation. Problems.

17. Earthquakes and Earthquake Ground Motion.

Causes of Earthquakes. Faults. Seismic Waves. Earthquake Intensity. Earthquake Magnitude. Seismicity. Earthquake Ground Motion. Earthquake Damage Mechanisms. References. Notation.

18. Earthquake Response of Structures.

Time-History Analysis: Basic Concepts. Earthquake Response Spectra. Earthquake Design Spectra. Response of MDOF Systems. Generalized SDOF Systems. In-Building Response Spectrum. Inelastic Response. Seismic Design Codes. References. Notation. Problems.

19. Blast Loads on Structures.

Sources of Blast Loads. Shock Waves. Determination of Blast Loads. Strain-Rate Effects. Approximate Solution Technique for SDOF Systems. References. Problems. Notations.

20. Basic Concepts of Wind Waves.

Linear Wave Theory. Nonlinear Waves. Wave Transformations. Wave Statistics. Wave Information Damping. References. Notation. Problems.

21. Response of Structures to Waves.

Morison Equation. Force Coefficients. Linearized Morison Equation. Inclined Cylinders. Transverse Lift Forces. Froude-Krylov Theory. Diffraction Theory: The Scattering Problem. Diffraction Theory: The Radiation Problem. References. Notation. Problems.

Appendix A.

Appendix B.

Index.