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| Preface | |
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| Equivalent Single-Degree-of-Freedom System and Free Vibration | |
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| Degrees of Freedom | |
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| Elements of a Vibratory System | |
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| Mass and/or Mass-Moment of Inertia | |
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| Pure Translational Motion | |
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| Pure Rotational Motion | |
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| Planar Motion (Combined Rotation and Translation) of a Rigid Body | |
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| Special Case: Pure Rotation about a Fixed Point | |
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| Spring | |
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| Pure Translational Motion | |
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| Pure Rotational Motion | |
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| Damper | |
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| Pure Translational Motion | |
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| Pure Rotational Motion | |
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| Equivalent Mass, Equivalent Stiffness, and Equivalent Damping Constant for an SDOF System | |
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| A Rotor-Shaft System | |
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| Equivalent Mass of a Spring | |
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| Springs in Series and Parallel | |
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| Springs in Series | |
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| Springs in Parallel | |
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| An SDOF System with Two Springs and Combined Rotational and Translational Motion | |
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| Viscous Dampers in Series and Parallel | |
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| Dampers in Series | |
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| Dampers in Parallel | |
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| Free Vibration of an Undamped SDOF System | |
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| Differential Equation of Motion | |
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| Energy Approach | |
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| Solution of the Differential Equation of Motion Governing Free Vibration of an Undamped Spring-Mass System | |
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| Free Vibration of a Viscously Damped SDOF System | |
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| Differential Equation of Motion | |
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| Solution of the Differential Equation of Motion Governing Free Vibration of a Damped Spring-Mass System | |
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| Underdamped (0 < � < 1 or 0 < C<sub>eq</sub> < c<sub>c</sub>) | |
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| Critically Damped (� = 1 or C<sub>eq</sub> = C<sub>c</sub>) | |
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| Overdamped (� > 1 or C<sub>eq</sub> > C<sub>c</sub>) | |
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| Logarithmic Decrement: Identification of Damping Ratio from Free Response of an Underdamped System (0 < � <1) | |
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| Solution | |
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| Stability of an SDOF Spring-Mass-Damper System | |
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| Exercise Problems | |
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| Vibration of a Single-Degree-of-Freedom System Under Constant and Purely Harmonic Excitation | |
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| Responses of Undamped and Damped SDOF Systems to a Constant Force | |
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| Undamped (� = 0) and Underdamped (0 <� <1) | |
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| Critically Damped (� > 1 or C<sub>eq</sub> = C<sub>c</sub>) | |
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| Overdamped (� > 1 or C<sub>eq</sub> > C<sub>c</sub>) | |
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| Response of an Undamped SDOF System to a Harmonic Excitation | |
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| � ≠ �<sub>n</sub> | |
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| � = �<sub>n</sub> (Resonance) | |
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| � ≠ �<sub>n</sub> | |
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| � = �<sub>n</sub> | |
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| Response of a Damped SDOF System to a Harmonic Excitation | |
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| Particular Solution | |
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| Underdamped (0 < � < 1 or 0 < C<sub>eq</sub> < C<sub>c</sub>) | |
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| Critically Damped (� = 1 or C<sub>eq</sub> = C<sub>c</sub>) | |
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| Overdamped (� > 1 or C<sub>eq</sub> > C<sub>c</sub>) | |
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| Steady State Response | |
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| Force Transmissibility | |
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| Quality Factor and Bandwidth | |
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| Quality Factor | |
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| Bandwidth | |
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| Rotating Unbalance | |
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| Base Excitation | |
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| Vibration Measuring Instruments | |
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| Vibrometer | |
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| Accelerometer | |
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| Equivalent Viscous Damping for Nonviscous Energy Dissipation | |
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| Exercise Problems | |
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| Responses of an SDOF Spring-Mass-Damper System to Periodic and Arbitrary Forces | |
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| Response of an SDOF System to a Periodic Force | |
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| Periodic Function and its Fourier Series Expansion | |
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| Even and Odd Periodic Functions | |
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| Fourier Coefficients for Even Periodic Functions | |
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| Fourier Coefficients for Odd Periodic Functions | |
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| Fourier Series Expansion of a Function with a Finite Duration | |
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| Particular Integral (Steady-State Response with Damping) Under Periodic Excitation | |
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| Response to an Excitation with Arbitrary Nature | |
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| Unit Impulse Function �(t - a) | |
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| Unit Impulse Response of an SDOF System with Zero Initial Conditions | |
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| Undamped and Underdamped System (0 ≤ � < 1) | |
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| Critically Damped (� = 1 or C<sub>eq</sub> = C<sub>c</sub>) | |
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| Overdamped (� > 1 or C<sub>eq</sub> > C<sub>c</sub>) | |
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| Convolution Integral: Response to an Arbitrary Excitation with Zero Initial Conditions | |
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| Convolution Integral: Response to an Arbitrary Excitation with Nonzero Initial Conditions | |
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| Undamped and Underdamped (0 ≤ � < 1 or 0 ≤ C<sub>eq</sub> < C<sub>c</sub>) | |
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| Critically Damped (� = 1 or C<sub>eq</sub> = C<sub>c</sub>) | |
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| Overdamped (� > 1 or C<sub>eq</sub> > C<sub>c</sub>) | |
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| Laplace Transformation | |
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| Properties of Laplace Transformation | |
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| Response of an SDOF System via Laplace Transformation | |
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| Transfer Function and Frequency Response Function | |
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| Significance of Transfer Function | |
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| Poles and Zeros of Transfer Function | |
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| Frequency Response Function | |
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| Exercise Problems | |
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| Vibration of Two-Degree-of-Freedom-Systems | |
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| Mass, Stiffness, and Damping Matrices | |
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| Natural Frequencies and Mode Shapes | |
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| Eigenvalue/Eigenvector Interpretation | |
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| Free Response of an Undamped 2DOF System Solution | |
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| Forced Response of an Undamped 2DOF System Under Sinusoidal Excitation | |
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| Free Vibration of a Damped 2DOF System | |
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| Steady-State Response of a Damped 2DOF System Under Sinusoidal Excitation | |
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| Vibration Absorber | |
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| Undamped Vibration Absorber | |
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| Damped Vibration Absorber | |
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| Tuned Case (f = 1 or �<sub>22</sub> = �<sub>11</sub>) | |
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| No restriction on f (Absorber not tuned to main system) | |
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| Modal Decomposition of Response | |
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| Undamped System (C = 0) | |
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| Damped System (C ≠ 0) | |
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| Exercise Problems | |
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| Finite and Infinite (Continuous) Dimensional Systems | |
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| Multi-Degree-of-Freedom Systems | |
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| Natural Frequencies and Modal Vectors (Mode Shapes) | |
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| Orthogonality of Eigenvectors for Symmetric Mass and Symmetric Stiffness Matrices | |
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| Modal Decomposition | |
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| Undamped System (C = 0) | |
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| Proportional or Rayleigh Damping | |
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| Continuous Systems Governed by Wave Equations | |
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| Transverse Vibration of a String | |
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| Natural Frequencies and Mode Shapes | |
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| Computation of Response | |
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| Longitudinal Vibration of a Bar | |
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| Torsional Vibration of a Circular Shaft | |
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| Continuous Systems: Transverse Vibration of a Beam | |
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| Governing Partical Differential Equation of Motion | |
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| Natural Frequencies and Mode Shapes | |
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| Simply Supported Beam | |
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| Cantilever Beam | |
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| Computation of Response | |
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| Finite Element Analysis | |
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| Longitudinal Vibration of a Bar | |
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| Total Kinetic and Potential Energies of the Bar | |
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| Transverse Vibration of a Beam | |
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| Total Kinetic and Potential Energies of the Beam | |
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| Exercise Problems | |
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| Equivalent Stiffnesses (Spring Constants) of Beams, Torsional Shaft, and Longitudinal Bar | |
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| Some Mathematical Formulae | |
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| Laplace Transform Table | |
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| References | |
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| Index | |