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| Introduction | |
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| The Study of Vibrations | |
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| Mathematical Modeling | |
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| Generalized Coordinates | |
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| Classification of Vibration | |
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| Dimensional Analysis | |
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| Simple Harmonic Motion | |
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| Review of Dynamics | |
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| Modeling of SDOF Systems | |
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| Introduction | |
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| Springs | |
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| Springs in Combination | |
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| Other Sources of Potential Energy | |
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| Viscous Damping | |
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| Energy Dissipated By Viscous Damping | |
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| Inertia Elements | |
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| External Sources | |
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| Free-Body Diagram Method | |
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| Static Deflections and Gravity | |
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| Small Angle or Displacement Assumption | |
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| Equivalent Systems Method | |
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| Free Vibrations of SDOF Systems | |
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| Introduction | |
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| Standard Form of Differential Equation | |
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| Free Vibrations of an Undamped System | |
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| Underdamped Free Vibrations | |
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| Critically Damped Free Vibrations | |
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| Overdamped Free Vibrations | |
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| Coulomb Damping | |
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| Hysteretic Damping | |
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| Other Forms of Damping | |
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| Harmonic Excitation of SDOF Systems | |
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| Introduction | |
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| Forced Response of an Undamped System Due to a Single-Frequency Excitation | |
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| Forced Response of a Viscously Damped System Subject to a Single-Frequency Harmonic Excitation | |
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| Frequency-squared Excitations | |
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| Response Sue to Harmonic Excitation of Support | |
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| Vibration Isolation | |
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| Vibration Isolation from Frequency-Squared Excitations | |
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| Practical Aspects of Vibration Isolation | |
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| Multifrequency Excitations | |
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| General Periodic Excitations | |
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| Seismic Vibration Measuring Instruments | |
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| Complex Representations | |
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| Systems with Coulomb Damping | |
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| Systems with Hysteretic Damping | |
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| Energy Harvesting | |
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| Transient Vibrations of One-Degree-Of-Freedom Systems | |
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| Introduction | |
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| Derivation of Convolution Integral | |
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| Response Due to a General Excitation | |
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| Excitations Whose Forms Change at Discrete Times | |
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| Transient Motion Due to Base Excitation | |
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| Laplace Transform Solutions | |
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| Transfer Functions | |
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| Numerical Methods | |
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| Shock Spectrum | |
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| Shock Isolation | |
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| Two-Degree-Of-Freedom Systems | |
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| Introduction | |
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| Derivation of the Equations of Motion | |
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| Natural Frequencies and Made Shapes | |
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| Free Response of Undamped Systems | |
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| Free Vibrations of a System with Viscous Damping | |
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| Principal Coordinates | |
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| Harmonic Response of Two-Degree-of Freedom Systems | |
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| Transfer Functions | |
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| Sinusoidal Transfer Function | |
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| Frequency Response | |
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| Dynamic Vibration Absorbers | |
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| Damped Vibration Absorbers | |
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| Vibration Dampers | |
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| Modeling of MDOF Systems | |
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| Introduction | |
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| Derivation of Differential Equations Using the Free-Body-Diagram Method | |
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| Lagrange�s Equations | |
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| Matrix Formulation of Differential Equations for Linear Systems | |
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| Stiffness Influence Coefficients | |
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| Flexibility Influence Coefficients | |
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| Inertia Influence Coefficients | |
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| Lumped-Mass Modeling of Continuous Systems | |
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| Free Vibrations of MDOF Systems | |
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| Introduction | |
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| Normal-Mode Solution | |
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| Natural Frequencies and Mode Shapes | |
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| General Solution | |
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| Special Cases | |
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| Energy Scalar Products | |
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| Properties of Natural Frequencies and Mode Shapes | |
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| Normalized Mode Shapes | |
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| Rayleigh�s Quotient | |
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| Forced Vibrations of MDOF Systems | |
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| Vibrations of Continuous Systems | |
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| Finite Element Method | |
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| Nonlinear Vibrations | |
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| Random Vibrations | |