PREFACE |
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xi | |
THE SI SYSTEM OF UNITS |
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1 | (4) |
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CHAPTER 1 OSCILLATORY MOTION |
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5 | (11) |
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6 | (3) |
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9 | (2) |
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1.3 Vibration Terminology |
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11 | (5) |
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16 | (33) |
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16 | (1) |
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2.2 Equation of Motion: Natural Frequency |
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16 | (4) |
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20 | (3) |
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2.4 Rayleigh Method: Effective Mass |
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23 | (2) |
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2.5 Principle of Virtual Work |
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25 | (2) |
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2.6 Viscously Damped Free Vibration |
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27 | (4) |
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2.7 Logarithmic Decrement |
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31 | (4) |
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35 | (14) |
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CHAPTER 3 HARMONICALLY EXCITED VIBRATION |
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49 | (40) |
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3.1 Forced Harmonic Vibration |
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49 | (4) |
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53 | (3) |
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56 | (3) |
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3.4 Whirling of Rotating Shafts |
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59 | (4) |
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63 | (2) |
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65 | (2) |
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3.7 Energy Dissipated by Damping |
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67 | (3) |
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3.8 Equivalent Viscous Damping |
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70 | (2) |
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72 | (2) |
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3.10 Sharpness of Resonance |
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74 | (1) |
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3.11 Vibration-Measuring Instruments |
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75 | (14) |
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CHAPTER 4 TRANSIENT VIBRATION |
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89 | (37) |
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89 | (2) |
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91 | (3) |
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4.3 Laplace Transform Formulation |
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94 | (3) |
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4.4 Pulse Excitation and Rise Time |
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97 | (3) |
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4.5 Shock Response Spectrum |
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100 | (4) |
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104 | (1) |
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4.7 Finite Difference Numerical Computation |
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105 | (7) |
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112 | (14) |
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CHAPTER 5 SYSTEMS WITH TWO OR MORE DEGREES OF FREEDOM |
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126 | (37) |
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5.1 The Normal Mode Analysis |
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127 | (4) |
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131 | (3) |
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134 | (5) |
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5.4 Forced Harmonic Vibration |
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139 | (2) |
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5.5 Finite Difference Method for Systems of Equations |
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141 | (3) |
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144 | (1) |
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5.7 Centrifugal Pendulum Vibration Absorber |
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145 | (2) |
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147 | (16) |
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CHAPTER 6 PROPERTIES OF VIBRATING SYSTEMS |
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163 | (36) |
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6.1 Flexibility Influence Coefficients |
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164 | (3) |
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167 | (5) |
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6.3 Stiffness Influence Coefficients |
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172 | (4) |
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6.4 Stiffness Matrix of Beam Elements |
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176 | (1) |
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6.5 Static Condensation for Pinned Joints |
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176 | (1) |
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6.6 Orthogonality of Eigenvectors |
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177 | (2) |
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179 | (2) |
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6.8 Decoupling Forced Vibration Equations |
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181 | (1) |
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6.9 Modal Damping in Forced Vibration |
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182 | (1) |
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6.10 Normal Mode Summation |
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183 | (4) |
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187 | (2) |
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6.12 Unrestrained (Degenerate) Systems |
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189 | (10) |
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CHAPTER 7 LAGRANGE'S EQUATION |
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199 | (28) |
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7.1 Generalized Coordinates |
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199 | (5) |
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204 | (3) |
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207 | (7) |
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7.4 Kinetic Energy, Potential Energy, and Generalized Force in Terms of Generalized Coordinates q |
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214 | (2) |
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7.5 Assumed Mode Summation |
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216 | (11) |
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CHAPTER 8 COMPUTATIONAL METHODS |
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227 | (41) |
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227 | (2) |
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8.2 Eigenvectors by Gauss Elimination |
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229 | (1) |
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230 | (3) |
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8.4 Convergence of the Iteration Procedure |
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233 | (1) |
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233 | (1) |
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8.6 Transformation Coordinates (Standard Computer Form) |
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234 | (1) |
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8.7 Systems with Discrete Mass Matrix |
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235 | (2) |
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8.8 Cholesky Decomposition |
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237 | (5) |
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8.9 Jacobi Diagonalization |
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242 | (5) |
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8.10 QR Method for Eigenvalue and Eigenvector Calculation |
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247 | (21) |
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CHAPTER 9 VIBRATION OF CONTINUOUS SYSTEMS |
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268 | (19) |
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268 | (3) |
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9.2 Longitudinal Vibration of Rods |
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271 | (2) |
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9.3 Torsional Vibration of Rods |
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273 | (3) |
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9.4 Vibration of Suspension Bridges |
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276 | (5) |
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9.5 Euler Equation for Beams |
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281 | (8) |
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9.6 System with Repeated Identical Sections |
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289 | |
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CHAPTER 10 INTRODUCTION TO THE FINITE ELEMENT METHOD |
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287 | (42) |
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10.1 Element Stiffness and Mass |
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287 | (5) |
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10.2 Stiffness and Mass for the Beam Element |
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292 | (3) |
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10.3 Transformation of Coordinates (Global Coordinates) |
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295 | (2) |
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10.4 Element Stiffness and Element Mass in Global Coordinates |
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297 | (5) |
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10.5 Vibrations Involving Beam Elements |
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302 | (7) |
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10.6 Spring Constraints on Structure |
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309 | (2) |
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10.7 Generalized Force for Distributed Load |
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311 | (2) |
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10.8 Generalized Force Proportional to Displacement |
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313 | (16) |
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CHAPTER 11 MODE-SUMMATION PROCEDURES FOR CONTINUOUS SYSTEMS |
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329 | (22) |
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11.1 Mode-Summation Method |
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329 | (6) |
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11.2 Normal Modes of Constrained Structures |
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335 | (4) |
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11.3 Mode-Acceleration Method |
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339 | (2) |
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11.4 Component-Mode Synthesis |
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341 | (10) |
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CHAPTER 12 CLASSICAL METHODS |
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351 | (44) |
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351 | (7) |
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12.2 Dunkerley's Equation |
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358 | (5) |
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12.3 Rayleigh-Ritz Method |
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363 | (3) |
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366 | (3) |
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12.5 Digital Computer Program for the Torsional System |
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369 | (2) |
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12.6 Myklestad's Method for Beams |
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371 | (4) |
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12.7 Coupled Flexure-Torsion Vibration |
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375 | (1) |
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376 | (2) |
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12.9 Systems with Damping |
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378 | (2) |
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380 | (1) |
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381 | (2) |
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12.12 Transfer Matrices for Beams |
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383 | (12) |
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CHAPTER 13 RANDOM VIBRATIONS |
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395 | (41) |
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395 | (1) |
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13.2 Time Averaging and Expected Value |
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396 | (2) |
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13.3 Frequency Response Function |
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398 | (3) |
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13.4 Probability Distribution |
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401 | (6) |
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407 | (4) |
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13.6 Power Spectrum and Power Spectral Density |
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411 | (6) |
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417 | (7) |
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424 | (12) |
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CHAPTER 14 NONLINEAR VIBRATIONS |
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436 | (26) |
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436 | (2) |
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14.2 Conservative Systems |
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438 | (3) |
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14.3 Stability of Equilibrium |
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441 | (2) |
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443 | (2) |
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445 | (3) |
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448 | (3) |
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14.7 Self-Excited Oscillations |
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451 | (2) |
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453 | (9) |
APPENDICES |
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462 | (44) |
A Specifications of Vibration Bounds |
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462 | (2) |
B Introduction to Laplace Transformation |
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464 | (5) |
C Determinants and Matirces |
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469 | (10) |
D Normal Modes of Uniform Beams |
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479 | (8) |
E Introduction to MATLAB(R) |
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487 | (5) |
F Computer Programs |
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492 | (9) |
G Convergence to Higher Modes |
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501 | (5) |
ANSWERS TO SELECTED PROBLEMS |
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506 | (13) |
INDEX |
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519 | |