ISBN: 3540645160
TITLE: Vibrations of Shells and Rods
AUTHOR: Le, Khanh C.
TOC:

1 Introduction 9
2 Preliminaries 17
2.1 Tensor analysis 17
2.2 Geometry of curves and surfaces 24
2.3 Dynamic theory of elasticity 30
2.4 Dynamic theory of piezoelectricity 37
2.5 Variational-asymptotic method 45
I Low-frequency vibrations 57
3 Elastic shells 59
3.1 Two-dimensional equations 59
3.2 Asymptotic analysis 68
3.3 Dispersion of waves in plates 78
3.4 Frequency spectra of circular plates 89
3.5 Dispersion of waves in cylindrical shells 96
3.6 Frequency spectra of cylindrical shells 109
3.7 Frequency spectra of spherical shells 118
4 Elastic rods 123
4.1 One-dimensional equations 123
4.2 Asymptotic analysis 130
4.3 Cross section problems 140
4.4 Dispersion of waves 147
4.5 Frequency spectra 155
5 Piezoelectric shells 163
5.1 Two-dimensional equations 163
5.2 Asymptotic analysis 172
5.3 Error estimation and comparison 183
5.4 Frequency spectra of circular plates 193
5.5 Frequency spectra of cylindrical shells 200
6 Piezoelectric rods 209
6.1 One-dimensional equations 209
6.2 Asymptotic analysis 215
6.3 Cross section problems 224
6.4 Frequency spectra 234
6.5 Longitudinal impact 240
II High-frequency vibrations 249
7 Elastic shells 251
7.1 Two-dimensional equations 251
7.2 Long-wave asymptotic analysis 257
7.3 Short-wave extrapolation 267
7.4 Dispersion of waves in plates 275
7.5 Frequency spectra of plates 285
7.6 Dispersion of waves in cylindrical shells 296
7.7 Frequency spectra of cylindrical shells 305
8 Elastic rods 311
8.1 One-dimensional equations 311
8.2 Long-wave asymptotic analysis 316
8.3 Short-wave extrapolation 322
8.4 Cross section problems 329
8.5 Dispersion of waves 336
8.6 Frequency spectra 340
9 Piezoelectric shells 349
9.1 Two-dimensional equations 349
9.2 Long-wave asymptotic analysis 351
9.3 Short-wave extrapolation 360
9.4 Frequency spectra of circular plates 369
9.5 Frequency spectra of cylindrical shells 374
10 Piezoelectric rods 381
10.1 One-dimensional equations 381
10.2 Long-wave asymptotic analysis 383
10.3 Short-wave extrapolation 390
10.4 Cross section problems 395
10.5 Frequency spectra 400
A Material constants 405
A.1 Elastic isotropic materials 405
A.2 Piezoelectric crystals 406
A.3 Piezoceramic materials 408
B List of notations 409
Bibliography 413
END
