Page 6 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)
P. 6
Contents
5.6 Vibration Absorber 150
5.7 Centrifugal Pendulum Vibration Absorber 152
5.8 Vibration Damper 154
6 PROPERTIES OF VIBRATING SYSTEMS 171
6.1 Flexibility Influence Coefficients 172
6.2 Reciprocity Theorem 175
6.3 Stiffness Influence Coefficients 176
6.4 Stiffness Matrix of Beam Elements 179
6.5 Static Condensation for Pinned Joints 183
6.6 Orthogonality of Eigenvectors 185
6.7 Modal Matrix P 187
6.8 Decoupling Forced Vibration Equations 189
6.9 Modal Damping in Forced Vibration 190
6.10 Normal Mode Summation 192
6.11 Equal Roots 195
6.12 Unrestrained (Degenerate) Systems 197
7 LAGRANGeS EQUATION 207
7.1 Generalized Coordinates 207
7.2 Virtual Work 212
7.3 Lagrange’s Equation 215
7.4 Kinetic Energy, Potential Energy, and Generalized
Force in Terms of Generalized Coordinates q 221
7.5 Assumed Mode Summation 223
a COMPUTATIONAL METHODS 234
8.1 Root Solving 235
8.2 Gauss Elimination 236
8.3 Matrix Iteration 238
8.4 Convergence of the Iteration Procedure 240
