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| Basic Concepts | |
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| Introduction to Structural Dynamics | |
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| Types of Dynamic Loads | |
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| Sources of Dynamic Loads | |
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| Distinguishing Features of a Dynamic Problem | |
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| Methodology for Dynamic Analysis | |
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| Types of Structural Vibration | |
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| Organization of the Text | |
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| Systems of Units | |
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| References | |
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| Single-Degree-of-Freedom (SDOF) Systems | |
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| Equation of Motion and Natural Frequency | |
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| Fundamental Components of a Vibrating System | |
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| D'Alembert's Principle of Dynamic Equilibrium | |
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| The Energy Method | |
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| The Principle of Virtual Displacements | |
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| References | |
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| Notation | |
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| Problems | |
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| Undamped Free Vibration | |
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| Simple Harmonic Motion | |
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| Interpretation of the Solution | |
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| Equivalent Stiffness | |
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| Rayleigh Method | |
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| References | |
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| Notation | |
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| Problems | |
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| 4 | |
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| Free Vibration with Viscous Damping | |
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| Logarithmic Decrement | |
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| Hysteresis Damping | |
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| Coulomb Damping | |
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| References | |
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| Notation | |
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| Problems | |
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| Response to Harmonic Excitation | |
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| Forced Harmonic Response of Undamped Systems | |
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| Beating and Resonance | |
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| Forced Harmonic Vibrations with Viscous Damping | |
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| Effect of Damping Factor on Steady-State Response and Phase Angle | |
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| Harmonic Excitation Caused by Rotating Unbalance | |
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| Base Excitation | |
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| Vibration Isolation and Transmissibility | |
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| References | |
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| Notation | |
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| Problems | |
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| Response to Periodic and Arbitrary Dynamic Excitation | |
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| Response to Periodic Excitation | |
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| Response to Unit Impulse | |
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| Duhamel Integral | |
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| Response to Arbitrary Dynamic Excitation | |
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| Response Spectrum | |
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| References | |
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| Notation | |
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| Problems | |
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| Numerical Evaluation of Dynamic Response | |
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| Interpolation of the Excitation | |
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| Direct Integration of the Equation of Motion | |
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| Central Difference Method | |
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| Runge-Kutta Methods | |
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| Average Acceleration Method | |
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| Linear Acceleration Method | |
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| Response to Base Excitation | |
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| Response Spectra by Numerical Integration | |
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| References | |
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| Notation | |
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| Problems | |
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| Frequency Domain Analysis | |
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| Alternative Forms of the Fourier Series | |
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| Discrete Fourier Transform | |
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| Fast Fourier Transform | |
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| Discrete Fourier Transform Implementation Considerations | |
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| Fourier Integral | |
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| References | |
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| Notation | |
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| Problems | |
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| Multi-Degree-of-Freedom (MDOF) Systems | |
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| General Property Matrices for Vibrating Systems | |
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| Flexibility Matrix | |
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| Stiffness Matrix | |
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| Inertia Properties: Mass Matrix | |
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| The Eigenproblem in Vibration Analysis | |
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| Static Condensation of the Stiffness Matrix | |
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| References | |
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| Notation | |
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| Problems | |
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| Equations of Motion and Undamped Free Vibration | |
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| Hamilton's Principle and the Lagrange Equations | |
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| Natural Vibration Frequencies | |
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| Natural Vibration Modes | |
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| Orthogonality of Natural Modes | |
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| Systems Admitting Rigid-Body Modes | |
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| Generalized Mass and Stiffness Matrices | |
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| Free Vibration Response to Initial Conditions | |
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| Approximate Methods for Estimating the Fundamental Frequency | |
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| References | |
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| Notation | |
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| Problems | |
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| Numerical Solution Methods for Natural Frequencies and Mode Shapes | |
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| General Solution Methods for Eigenproblems | |
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| Inverse Vector Iteration | |
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| Forward Vector Iteration | |
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| Generalized Jacobi Method | |
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| Solution Methods for Large Eigenproblems | |
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| References | |
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| Notation | |
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| Problems | |