| Preface |
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Vibrations of Thin Elastic Plates and Classical Point Models |
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1 | (62) |
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Kirchhoff model for flexural waves |
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1 | (8) |
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Fundamentals of elasticity |
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1 | (1) |
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Flexural deformations of thin plates |
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2 | (4) |
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Differential operator and boundary conditions |
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6 | (1) |
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7 | (2) |
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9 | (3) |
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Scattering problems and general properties of solutions |
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12 | (22) |
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12 | (2) |
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Green's function of unperturbed problem |
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14 | (5) |
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19 | (3) |
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22 | (6) |
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Uniqueness of the solution |
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28 | (4) |
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Flexural wave concentrated near a circular hole |
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32 | (2) |
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34 | (19) |
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Point models in two dimensions |
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34 | (11) |
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Scattering by crack at oblique incidence |
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45 | (4) |
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Point models in three dimensions |
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49 | (4) |
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Scattering problems for plates with infinite crack |
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53 | (10) |
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General properties of boundary value problems |
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53 | (1) |
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Scattering problems in isolated plates |
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54 | (6) |
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Scattering by pointwise joint |
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60 | (3) |
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Operator Methods in Diffraction |
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63 | (44) |
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63 | (13) |
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63 | (4) |
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67 | (1) |
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Adjoint, symmetric and selfadjoint operators |
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68 | (3) |
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71 | (5) |
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Space L2 and differential operators |
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76 | (6) |
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76 | (4) |
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80 | (1) |
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Sobolev spaces and embedding theorems |
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81 | (1) |
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82 | (8) |
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82 | (2) |
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84 | (1) |
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Operator of fluid loaded plate |
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85 | (4) |
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Another operator model of fluid loaded plate |
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89 | (1) |
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Extensions theory for differential operators |
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90 | (17) |
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Zero range potentials for harmonic operator |
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91 | (3) |
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Zero range potentials for bi-harmonic operator |
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94 | (4) |
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Zero range potentials for fluid loaded plates |
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98 | (6) |
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Zero range potentials for the plate with infinite crack |
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104 | (3) |
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107 | (90) |
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Shortages of classical point models and the general procedure of generalized models construction |
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107 | (5) |
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112 | (25) |
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112 | (1) |
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The case of absolutely rigid plate |
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113 | (2) |
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The case of isolated plate |
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115 | (1) |
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Generalized point model of narrow crack |
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115 | (2) |
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Scattering by point model of narrow crack |
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117 | (6) |
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Diffraction by a crack of finite width in fluid loaded elastic plate |
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123 | (9) |
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Discussion and numerical results |
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132 | (5) |
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137 | (29) |
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Diffraction by a short crack in isolated plate |
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138 | (14) |
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Generalized point model of short crack |
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152 | (5) |
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Scattering by the generalized point model of short crack |
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157 | (4) |
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Diffraction by a short crack in fluid loaded plate |
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161 | (4) |
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165 | (1) |
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Model of small circular hole |
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166 | (11) |
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The case of absolutely rigid plate |
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166 | (2) |
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The case of isolated plate |
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168 | (5) |
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173 | (3) |
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Other models of circular holes |
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176 | (1) |
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Model of narrow joint of two semi-infinite plates |
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177 | (20) |
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177 | (3) |
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180 | (7) |
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187 | (3) |
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Scattering by the generalized model of narrow joint |
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190 | (7) |
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Discussions and Recommendations for Future Research |
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197 | (32) |
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General properties of models |
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197 | (8) |
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Generalized models in two dimensions |
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198 | (5) |
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Structure of generalized models in three dimensions |
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203 | (2) |
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Generalized models in the plate with infinite crack |
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205 | (1) |
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Extending of the model of narrow crack to oblique incidence and edge wave analysis |
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205 | (7) |
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Reformulation of the model |
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205 | (2) |
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Edge waves propagating along a narrow crack |
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207 | (5) |
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Further generalizations and unsolved problems |
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212 | (5) |
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Models with internal structure |
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212 | (1) |
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213 | (3) |
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216 | (1) |
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Other approximate theories of vibrations |
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216 | (1) |
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Model of protruding stiffener in elastic plate |
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217 | (12) |
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217 | (1) |
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217 | (1) |
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218 | (4) |
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Scattering by the zero-range potential |
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222 | (2) |
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Choice of parameters in the model |
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224 | (3) |
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Generalized model of protruding stiffener in fluid loaded plate |
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227 | (2) |
| Appendix A Regularization and Analysis of Boundary-Contact Integrals |
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229 | (10) |
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A.1 Boundary-contact integrals in two dimensional problems |
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229 | (3) |
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A.2 Boundary-contact integrals for oblique incidence |
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232 | (1) |
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A.3 Low frequency asymptotics |
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233 | (1) |
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A.4 Boundary-contact integrals in three dimensions |
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234 | (2) |
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A.5 Boundary-contact integrals for the plate with infinite crack |
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236 | (3) |
| Appendix B Integral Equations of Convolution on a Finite Interval |
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239 | (12) |
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B.1 Integral equations of convolution |
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239 | (1) |
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B.2 Logarithmic singularity of the kernel |
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240 | (5) |
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B.3 Supersingular kernels |
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245 | (3) |
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248 | (3) |
| Appendix C Models Used for Numerical Analysis |
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251 | (2) |
| Bibliography |
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253 | (6) |
| Index |
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259 | |
Rohkem infot World Scientific e-raamatute kohta