Preface xi Acknowledgement xiii About the Companion Website xv 1 Sign Conventions and Equations of Motion Derivations 1 1.1 Derivation of the Bending Equations of Motion by Various Sign Conventions 1 1.1.1 According to Euler-Bernoulli Bending Vibration Theory 2 1.1.2 According to Timoshenko Bending Vibration Theory 7 1.2 Derivation of the Elementary Longitudinal Equation of Motion by Various Sign Conventions 10 1.3 Derivation of the Elementary Torsional Equation of Motion by Various Sign Conventions 12 2 Longitudinal Waves in Beams 15 2.

1 The Governing Equation and the Propagation Relationships 15 2.2 Wave Reflection at Classical and Non-Classical Boundaries 16 2.3 Free Vibration Analysis in Finite Beams - Natural Frequencies and Modeshapes 20 2.4 Force Generated Waves and Forced Vibration Analysis of Finite Beams 24 2.5 Numerical Examples and Experimental Studies 27 2.6 MATLAB Scripts 32 3 Bending Waves in Beams 39 3.1 The Governing Equation and the Propagation Relationships 39 3.2 Wave Reflection at Classical and Non-Classical Boundaries 40 3.

3 Free Vibration Analysis in Finite Beams - Natural Frequencies and Modeshapes 46 3.4 Force Generated Waves and Forced Vibration Analysis of Finite Beams 50 3.5 Numerical Examples and Experimental Studies 55 3.6 MATLAB Scripts 59 4 Waves in Beams on a Winkler Elastic Foundation 69 4.1 Longitudinal Waves in Beams 69 4.1.1 The Governing Equation and the Propagation Relationships 69 4.1.

2 Wave Reflection at Boundaries 70 4.1.3 Free Wave Vibration Analysis 71 4.1.4 Force Generated Waves and Forced Vibration Analysis of Finite Beams 72 4.1.5 Numerical Examples 76 4.2 Bending Waves in Beams 79 4.

2.1 The Governing Equation and the Propagation Relationships 79 4.2.2 Wave Reflection at Classical Boundaries 82 4.2.3 Free Wave Vibration Analysis 84 4.2.4 Force Generated Waves and Forced Wave Vibration Analysis 84 4.

2.5 Numerical Examples 89 ftoc.indd 7 29-06-2023 20:15:06 5 Coupled Waves in Composite Beams 97 5.1 The Governing Equations and the Propagation Relationships 97 5.2 Wave Reflection at Classical and Non-Classical Boundaries 100 5.3 Wave Reflection and Transmission at a Point Attachment 102 5.4 Free Vibration Analysis in Finite Beams - Natural Frequencies and Modeshapes 104 5.5 Force Generated Waves and Forced Vibration Analysis of Finite Beams 105 5.

6 Numerical Examples 108 5.7 MATLAB Script 114 6 Coupled Waves in Curved Beams 119 6.1 The Governing Equations and the Propagation Relationships 119 6.2 Wave Reflection at Classical and Non-Classical Boundaries 121 6.3 Free Vibration Analysis in a Finite Curved Beam - Natural Frequencies and Modeshapes 127 6.4 Force Generated Waves and Forced Vibration Analysis of Finite Curved Beams 128 6.5 Numerical Examples 134 6.6 MATLAB Scripts 143 7 Flexural/Bending Vibration of Rectangular Isotropic Thin Plates with Two Opposite Edges Simply-supported 151 7.

1 The Governing Equations of Motion 151 7.2 Closed-form Solutions 152 7.3 Wave Reflection, Propagation, and Wave Vibration Analysis Along the Simply-supported X Direction 154 7.4 Wave Reflection, Propagation, and Wave Vibration Analysis Along the y Direction 156 7.4.1 Wave Reflection at a Classical Boundary along the y Direction 157 7.4.2 Wave Propagation and Wave Vibration Analysis along the y Direction 159 7.

5 Numerical Examples 159 8 In-Plane Vibration of Rectangular Isotropic Thin Plates with Two Opposite Edges Simply-supported 189 8.1 The Governing Equations of Motion 189 8.2 Closed-form Solutions 190 8.3 Wave Reflection, Propagation, and Wave Vibration Analysis along the Simply-supported X Direction 192 8.3.1 Wave Reflection at a Simply-supported Boundary Along the X Direction 192 8.3.2 Wave Propagation and Wave Vibration Analysis Along the X Direction 195 8.

4 Wave Reflection, Propagation, and Wave Vibration Analysis along the y Direction 197 8.4.1 Wave Reflection at a Classical Boundary along the y Direction 198 8.4.2 Wave Propagation and Wave Vibration Analysis along the y Direction 201 8.5 Special Situation of k 0 = 0: Wave Reflection, Propagation, and Wave Vibration Analysis along the y Direction 201 8.5.1 Wave Reflection at a Classical Boundary along the y Direction Corresponding to a Pair of Type I Simple Supports Along the X Direction When K 0 = 0 202 8.

5.2 Wave Reflection at a Classical Boundary along the y Direction Corresponding to a Pair of Type II Simple Supports Along the X Direction When K 0 = 0 203 8.5.3 Wave Propagation and Wave Vibration Analysis along the y Direction When k 0 = 0 205 8.6 Wave Reflection, Propagation, and Wave Vibration Analysis with a Pair of Simply-supported Boundaries along the y Direction When k 0 ≠ 0 207 8.6.1 Wave Reflection, Propagation, and Wave Vibration Analysis with a Pair of Simply-supported Boundaries along the y Direction When k 0 ≠ 0, k 1 ≠ 0, and k 2 ≠ 0 207 8.6.

2 Wave Reflection, Propagation, and Wave Vibration Analysis with a Pair of Simply-supported Boundaries along the y Direction When k 0 = 0, and either k 1 = 0 or k 2 = 0 209 8.7 Numerical Examples 212 8.7.1 Example 1: Two Pairs of the Same Type of Simple Supports Along the X and Y Directions 212 8.7.2 Example 2: One Pair of the Same Type Simple Supports Along the X Direction, Various Combinations of Classical Boundaries on Opposite Edges along the y Direction 217 8.7.3 Example 3: One Pair of Mixed Type Simple Supports Along the X Direction, Various Combinations of Classical Boundaries on Opposite Edges along the y Direction 223 9 Bending Waves in Beams Based on Advanced Vibration Theories 227 9.

1 The Governing Equations and the Propagation Relationships 227 9.1.1 Rayleigh Bending Vibration Theory 227 9.1.2 Shear Bending Vibration Theory 228 9.1.3 Timoshenko Bending Vibration Theory 230 9.2 Wave Reflection at Classical and Non-Classical Boundaries 232 9.

2.1 Rayleigh Bending Vibration Theory 232 9.2.2 Shear and Timoshenko Bending Vibration Theories 238 9.3 Waves Generated by Externally Applied Point Force and Moment on the Span 244 9.3.1 Rayleigh Bending Vibration Theory 245 9.3.

2 Shear and Timoshenko Bending Vibration Theories 246 9.4 Waves Generated by Externally Applied Point Force and Moment at a Free End 247 9.4.1 Rayleigh Bending Vibration Theory 248 9.4.2 Shear and Timoshenko Bending Vibration Theories 249 9.5 Free and Forced Vibration Analysis 250 9.5.

1 Free Vibration Analysis 250 9.5.2 Forced Vibration Analysis 250 9.6 Numerical Examples and Experimental Studies 252 9.7 MATLAB Scripts 257 10 Longitudinal Waves in Beams Based on Various Vibration Theories 263 10.1 The Governing Equations and the Propagation Relationships 263 10.1.1 Love Longitudinal Vibration Theory 263 10.

1.2 Mindlin-Herrmann Longitudinal Vibration Theory 264 10.1.3 Three-mode Longitudinal Vibration Theory 265 10.2 Wave Reflection at Classical Boundaries 267 10.2.1 Love Longitudinal Vibration Theory 267 10.2.

2 Mindlin-Herrmann Longitudinal Vibration Theory 268 10.2.3 Three-mode Longitudinal Vibration Theory 269 10.3 Waves Generated by External Excitations on the Span 271 10.3.1 Love Longitudinal Vibration Theory 271 10.3.2 Mindlin-Herrmann Longitudinal Vibration Theory 272 10.

3.3 Three-mode Longitudinal Vibration Theory 273 10.4 Waves Generated by External Excitations at a Free End 275 10.4.1 Love Longitudinal Vibration Theory 275 10.4.2 Mindlin-Herrmann Longitudinal Vibration Theory 276 10.4.

3 Three-mode Longitudinal Vibration Theory 276 10.5 Free and Forced Vibration Analysis 277 10.5.1 Free Vibration Analysis 278 10.5.2 Forced Vibration Analysis 278 10.6 Numerical Examples and Experimental Studies 281 11 Bending and Longitudinal Waves in Built-up Planar Frames 287 11.1 The Governing Equations and the Propagation Relationships 287 11.

2 Wave Reflection at Classical Boundaries 289 11.3 Force Generated Waves 291 11.4 Free and Forced Vibration Analysis of a Multi-story Multi-bay Planar Frame 292 11.5 Reflection and Transmission of Waves in a Multi-story Multi-bay Planar Frame 304 11.5.1 Wave Reflection and Transmission at an L-shaped Joint 304 11.5.2 Wave Reflection and Transmission at a T-shaped Joint 308 11.

5.3 Wave Reflection and Transmission at a Cross Joint 315 12 Bending, Longitudinal, and Torsional Waves in Built-up Space Frames 329 12.1 The Governing Equations and the Propagation Relationships 329 12.2 Wave Reflection at Classical Boundaries 333 12.3 Force Generated Waves 336 12.4 Free and Forced Vibration Analysis of a Multi-story Space Frame 338 12.5 Reflection and Transmission of Waves in a Multi-story Space Frame 341 12.5.

1 Wave Reflection and Transmission at a Y-shaped Spatial Joint 343 12.5.2 Wave Reflection and Transmission at a K-shaped Spatial Joint 353 13 Passive Wave Vibration Control 369 13.1 Change in Cross Section or Material 369 13.1.1 Wave Reflection and Transmission at a Step Change by Euler-Bernoulli Bending Vibration Theory 371 13.1.2 Wave Reflection and Transmission at a Step Change by Timoshenko B.