1 Introduction ................................................. 1
2 Coupled Thermoelasticity and Transonic Gas Flow ............. 15
2.1 Coupled Linear Thermoelasticity of Shallow Shells ...... 16
2.1.1 Fundamental Assumptions ......................... 16
2.1.2 Differential Equations .......................... 18
2.1.3 Boundary and Initial Conditions ................. 21
2.1.4 An Abstract Coupled Problem ..................... 24
2.1.5 Existence and Uniqueness of Solutions
of Thermoelasticity Problems .................... 31
2.2 Cylindrical Panel Within Transonic Gas Flow ............ 43
2.2.1 Statement and Solution of the Problem ........... 43
2.2.2 Stable Vibrating Panel Within a Transonic
Flow ............................................ 85
2.2.3 Stability Loss of Panel Within Transonic Flow ... 99
3 Estimation of the Errors of the Bubnov-Galerkin Method ..... 115
3.1 An Abstract Coupled Problem ........................... 115
3.2 Coupled Thermoelastic Problem Within the Kirchhoff-
Love Model ............................................ 134
3.3 Case of a Simply Supported Plate Within
the Kirchhoff Model ................................... 146
3.4 Coupled Problem of Thermoelasticity Within
a Timoshenko-Type Model ............................... 159
4 Numerical Investigations of the Errors of the Bubnov-
Galerkin Method ............................................ 165
4.1 Vibration of a Transversely Loaded Plate .............. 165
4.2 Vibration of a Plate with an Imperfection in the
Form of a Deflection .................................. 172
4.3 Vibration of a Plate with a Given Variable
Deflection Change ..................................... 176
5 Coupled Nonlinear Thermoelastic Problems ................... 179
5.1 Fundamental Relations and Assumptions ................. 179
5.2 Differential Equations ................................ 182
5.3 Boundary and Initial Conditions ....................... 188
5.4 On the Existence and Uniqueness of a Solution ......... 189
6 Theory with Physical Nonlinearities and Coupling ........... 217
6.1 Fundamental Assumptions and Relations ................. 217
6.2 Variational Equations of Physically Nonlinear
Coupled Problems ...................................... 220
6.3 Equations in Terms of Displacements ................... 224
7 Nonlinear Problems of Hybrid-Form Equations ................ 229
7.1 Method of Solution for Nonlinear Coupled Problems ..... 230
7.2 Relaxation Method ..................................... 235
7.3 Numerical Investigations and Reliability
of the Results Obtained ............................... 243
7.4 Vibration of Isolated Shell Subjected to Impulse ...... 249
7.5 Dynamic Stability of Shells Under Thermal Shock ....... 270
7.6 Influence of Coupling and Rotational Inertia on
Stability ............................................. 290
7.7 Numerical Tests ....................................... 301
7.8 Influence of Damping e and Excitation Amplitude A ..... 305
7.9 Spatial-Temporal Symmetric Chaos ...................... 309
7.10 Dissipative Nonsymmetric Oscillations ................. 327
7.11 Solitary Waves ........................................ 332
8 Dynamics of Thin Elasto-Plastic Shells ..................... 349
8.1 Fundamental Relations ................................. 349
8.2 Method of Solution .................................... 355
8.3 Oscillations and Stability of Elasto-Plastic Shells ... 359
9 Unsolved Problems in Nonlinear Dynamics of Shells .......... 391
References .................................................... 405
Index ......................................................... 419
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