Page 7 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)
P. 7
Contents
8.5 Convergence to Higher Modes 241
8.6 The Dynamic Matrix 246
8.7 Transformation of Coordinates (Standard Computer
Form) 247
8.8 Systems with Discrete Mass Matrix 248
8.9 Cholesky Decomposition 249
8.10 Jacobi Diagonalization 253
8.11 Computer Program Notes 260
8.12 Description of Computer Programs 261
9 VIBRATION OF CONTINUOUS SYSTEMS 268
9.1 Vibrating String 268
9.2 Longitudinal Vibration of Rods 271
9.3 Torsional Vibration of Rods 273
9.4 Vibration of Suspension Bridges 276
9.5 Euler Equation for Beams 281
9.6 Effect of Rotary Inertia and Shear
Deformation 286
9.7 System with Repeated Identical Sections 289
10 INTRODUCTION TO THE FINITE ELEMENT METHOD 301
10.1 Element Stiffness and Mass 301
10.2 Stiffness and Mass for the Beam Element 306
10.3 Transformation of Coordinates
(Global Coordinates) 309
10.4 Element Stiffness and Element Mass
in Global Coordinates 312
10.5 Vibrations Involving Beam Elements 317
10.6 Spring Constraints on Structure 324
10.7 Generalized Force for Distributed Load 327
10.8 Generalized Force Proportional to Displacement
328
