| Preface | p. xiii |
| Equivalent Single-Degree-of-Freedom System and Free Vibration | p. 1 |
| Degrees of Freedom | p. 3 |
| Elements of a Vibratory System | p. 5 |
| Mass and/or Mass-Moment of Inertia | p. 5 |
| Pure Translational Motion | p. 5 |
| Pure Rotational Motion | p. 6 |
| Planar Motion (Combined Rotation and Translation) of a Rigid Body | p. 6 |
| Special Case: Pure Rotation about a Fixed Point | p. 8 |
| Spring | p. 8 |
| Pure Translational Motion | p. 8 |
| Pure Rotational Motion | p. 9 |
| Damper | p. 10 |
| Pure Translational Motion | p. 10 |
| Pure Rotational Motion | p. 11 |
| Equivalent Mass, Equivalent Stiffness, and Equivalent Damping Constant for an SDOF System | p. 12 |
| A Rotor-Shaft System | p. 13 |
| Equivalent Mass of a Spring | p. 14 |
| Springs in Series and Parallel | p. 16 |
| Springs in Series | p. 16 |
| Springs in Parallel | p. 17 |
| An SDOF System with Two Springs and Combined Rotational and Translational Motion | p. 19 |
| Viscous Dampers in Series and Parallel | p. 22 |
| Dampers in Series | p. 22 |
| Dampers in Parallel | p. 23 |
| Free Vibration of an Undamped SDOF System | p. 25 |
| Differential Equation of Motion | p. 25 |
| Energy Approach | p. 27 |
| Solution of the Differential Equation of Motion Governing Free Vibration of an Undamped Spring-Mass System | p. 34 |
| Free Vibration of a Viscously Damped SDOF System | p. 40 |
| Differential Equation of Motion | p. 40 |
| Solution of the Differential Equation of Motion Governing Free Vibration of a Damped Spring-Mass System | p. 41 |
| Underdamped (0 < < 1 or 0 < Ceq < cc) | p. 42 |
| Critically Damped ( = 1 or Ceq = Cc) | p. 45 |
| Overdamped ( > 1 or Ceq > Cc) | p. 46 |
| Logarithmic Decrement: Identification of Damping Ratio from Free Response of an Underdamped System (0 < <1) | p. 51 |
| Solution | p. 55 |
| Stability of an SDOF Spring-Mass-Damper System | p. 58 |
| Exercise Problems | p. 63 |
| Vibration of a Single-Degree-of-Freedom System Under Constant and Purely Harmonic Excitation | p. 72 |
| Responses of Undamped and Damped SDOF Systems to a Constant Force | p. 72 |
| Undamped ( = 0) and Underdamped (0 < <1) | p. 74 |
| Critically Damped ( > 1 or Ceq = Cc) | p. 75 |
| Overdamped ( > 1 or Ceq > Cc) | p. 76 |
| Response of an Undamped SDOF System to a Harmonic Excitation | p. 82 |
| ≠ n | p. 83 |
| = n (Resonance) | p. 84 |
| ≠ n | p. 87 |
| = n | p. 87 |
| Response of a Damped SDOF System to a Harmonic Excitation | p. 88 |
| Particular Solution | p. 89 |
| Underdamped (0 < < 1 or 0 < Ceq < Cc) | p. 92 |
| Critically Damped ( = 1 or Ceq = Cc) | p. 92 |
| Overdamped ( > 1 or Ceq > Cc) | p. 94 |
| Steady State Response | p. 95 |
| Force Transmissibility | p. 101 |
| Quality Factor and Bandwidth | p. 106 |
| Quality Factor | p. 106 |
| Bandwidth | p. 107 |
| Rotating Unbalance | p. 109 |
| Base Excitation | p. 116 |
| Vibration Measuring Instruments | p. 121 |
| Vibrometer | p. 123 |
| Accelerometer | p. 126 |
| Equivalent Viscous Damping for Nonviscous Energy Dissipation | p. 128 |
| Exercise Problems | p. 132 |
| Responses of an SDOF Spring-Mass-Damper System to Periodic and Arbitrary Forces | p. 138 |
| Response of an SDOF System to a Periodic Force | p. 138 |
| Periodic Function and its Fourier Series Expansion | p. 139 |
| Even and Odd Periodic Functions | p. 142 |
| Fourier Coefficients for Even Periodic Functions | p. 143 |
| Fourier Coefficients for Odd Periodic Functions | p. 145 |
| Fourier Series Expansion of a Function with a Finite Duration | p. 147 |
| Particular Integral (Steady-State Response with Damping) Under Periodic Excitation | p. 151 |
| Response to an Excitation with Arbitrary Nature | p. 154 |
| Unit Impulse Function (t - a) | p. 155 |
| Unit Impulse Response of an SDOF System with Zero Initial Conditions | p. 156 |
| Undamped and Underdamped System (0 ≤ < 1) | p. 158 |
| Critically Damped ( = 1 or Ceq = Cc) | p. 158 |
| Overdamped ( > 1 or Ceq > Cc) | p. 159 |
| Convolution Integral: Response to an Arbitrary Excitation with Zero Initial Conditions | p. 160 |
| Convolution Integral: Response to an Arbitrary Excitation with Nonzero Initial Conditions | p. 165 |
| Undamped and Underdamped (0 ≤ < 1 or 0 ≤ Ceq < Cc) | p. 166 |
| Critically Damped ( = 1 or Ceq = Cc) | p. 166 |
| Overdamped ( > 1 or Ceq > Cc) | p. 166 |
| Laplace Transformation | p. 168 |
| Properties of Laplace Transformation | p. 169 |
| Response of an SDOF System via Laplace Transformation | p. 170 |
| Transfer Function and Frequency Response Function | p. 173 |
| Significance of Transfer Function | p. 175 |
| Poles and Zeros of Transfer Function | p. 175 |
| Frequency Response Function | p. 176 |
| Exercise Problems | p. 179 |
| Vibration of Two-Degree-of-Freedom-Systems | p. 186 |
| Mass, Stiffness, and Damping Matrices | p. 187 |
| Natural Frequencies and Mode Shapes | p. 192 |
| Eigenvalue/Eigenvector Interpretation | p. 197 |
| Free Response of an Undamped 2DOF System Solution | p. 200 |
| Forced Response of an Undamped 2DOF System Under Sinusoidal Excitation | p. 201 |
| Free Vibration of a Damped 2DOF System | p. 203 |
| Steady-State Response of a Damped 2DOF System Under Sinusoidal Excitation | p. 209 |
| Vibration Absorber | p. 212 |
| Undamped Vibration Absorber | p. 212 |
| Damped Vibration Absorber | p. 220 |
| Tuned Case (f = 1 or 22 = 11) | p. 224 |
| No restriction on f (Absorber not tuned to main system) | p. 224 |
| Modal Decomposition of Response | p. 227 |
| Undamped System (C = 0) | p. 228 |
| Damped System (C ≠ 0) | p. 228 |
| Exercise Problems | p. 231 |
| Finite and Infinite (Continuous) Dimensional Systems | p. 237 |
| Multi-Degree-of-Freedom Systems | p. 237 |
| Natural Frequencies and Modal Vectors (Mode Shapes) | p. 239 |
| Orthogonality of Eigenvectors for Symmetric Mass and Symmetric Stiffness Matrices | p. 242 |
| Modal Decomposition | p. 245 |
| Undamped System (C = 0) | p. 246 |
| Proportional or Rayleigh Damping | p. 249 |
| Continuous Systems Governed by Wave Equations | p. 250 |
| Transverse Vibration of a String | p. 250 |
| Natural Frequencies and Mode Shapes | p. 251 |
| Computation of Response | p. 255 |
| Longitudinal Vibration of a Bar | p. 258 |
| Torsional Vibration of a Circular Shaft | p. 261 |
| Continuous Systems: Transverse Vibration of a Beam | p. 265 |
| Governing Partical Differential Equation of Motion | p. 265 |
| Natural Frequencies and Mode Shapes | p. 267 |
| Simply Supported Beam | p. 269 |
| Cantilever Beam | p. 271 |
| Computation of Response | p. 273 |
| Finite Element Analysis | p. 279 |
| Longitudinal Vibration of a Bar | p. 279 |
| Total Kinetic and Potential Energies of the Bar | p. 283 |
| Transverse Vibration of a Beam | p. 286 |
| Total Kinetic and Potential Energies of the Beam | p. 291 |
| Exercise Problems | p. 295 |
| Equivalent Stiffnesses (Spring Constants) of Beams, Torsional Shaft, and Longitudinal Bar | p. 299 |
| Some Mathematical Formulae | p. 302 |
| Laplace Transform Table | p. 304 |
| References | p. 305 |
| Index | p. 307 |
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