Contents -- Preface -- Chapter 1 Vibrations of Thin Elastic Plates and Classical Point Models -- 1.1 Kirchhoff model for flexural waves -- 1.1.1 Fundamentals of elasticity -- 1.1.2 Flexural deformations of thin plates -- 1.1.3 Differential operator and boundary conditions -- 1.1.4 Flexural waves -- 1.2 Fluid loaded plates -- 1.3 Scattering problems and general properties of solutions -- 1.3.1 Problem formulation -- 1.3.2 Green's function of unperturbed problem -- 1.3.3 Integral representation -- 1.3.4 Optical theorem -- 1.3.5 Uniqueness of the solution -- 1.3.6 Flexural wave concentrated near a circular hole -- 1.4 Classical point models -- 1.4.1 Point models in two dimensions -- 1.4.2 Scattering by crack at oblique incidence -- 1.4.3 Point models in three dimensions -- 1.5 Scattering problems for plates with infinite crack -- 1.5.1 General properties of boundary value problems -- 1.5.2 Scattering problems in isolated plates -- 1.5.3 Scattering by pointwise joint -- Chapter 2 Operator Methods in Diffraction -- 2.1 Abstract operator theory -- 2.1.1 Hilbert space -- 2.1.2 Operators -- 2.1.3 Adjoint symmetric and selfadjoint operators -- 2.1.4 Extension theory -- 2.2 Space L2 and differential operators -- 2.2.1 Hilbert space L2 -- 2.2.2 Generalized derivatives -- 2.2.3 Sobolev spaces and embedding theorems -- 2.3 Problems of scattering -- 2.3.1 Harmonic operator -- 2.3.2 Bi-harmonic operator -- 2.3.3 Operator of fluid loaded plate -- 2.3.4 Another operator model of fluid loaded plate -- 2.4 Extensions theory for differential operators -- 2.4.1 Zero-range potentials for harmonic operator -- 2.4.2 Zero-range potentials for bi-harmonic operator -- 2.4.3 Zero-range potentials for fluid loaded plates -- 2.4.4 Zero-range potentials for the plate with infinite crack -- Chapter 3 Generalized Point Models.

3.1 Shortages of classical point models and the general procedure of generalized models construction -- 3.2 Model of narrow crack -- 3.2.1 Introduction -- 3.2.2 The case of absolutely rigid plate -- 3.2.3 The case of isolated plate -- 3.2.4 Generalized point model of narrow crack -- 3.2.5 Scattering by point model of narrow crack -- 3.2.6 Diffraction by a crack of finite width in fluid loaded elastic plate -- 3.2.7 Discussion and numerical results -- 3.3 Model of a short crack -- 3.3.1 Diffraction by a short crack in isolated plate -- 3.3.2 Generalized point model of short crack -- 3.3.3 Scattering by the generalized point model of short crack -- 3.3.4 Diffraction by a short crack in fluid loaded plate -- 3.3.5 Discussion -- 3.4 Model of small circular hole -- 3.4.1 The case of absolutely rigid plate -- 3.4.2 The case of isolated plate -- 3.4.3 Generalized point model -- 3.4.4 Other models of circular holes -- 3.5 Model of narrow joint of two semi-infinite plates -- 3.5.1 Problem formulation -- 3.5.2 Isolated plate -- 3.5.3 Generalized model -- 3.5.4 Scattering by the generalized model of narrow joint -- Chapter 4 Discussions and Recommendations for Future Research -- 4.1 General properties of models -- 4.1.1 Generalized models in two dimensions -- 4.1.2 Structure of generalized models in three dimensions -- 4.1.3 Generalized models in the plate with infinite crack -- 4.2 Extending of the model of narrow crack to oblique incidence and edge wave analysis -- 4.2.1 Reformulation of the model -- 4.2.2 Edge waves propagating along a narrow crack -- 4.3 Further generalizations and unsolved problems -- 4.3.1 Models with internal structure -- 4.3.2 Restrictions of accuracy -- 4.3.3 Other basic geometry -- 4.3.4 Other approximate theories of vibrations.

4.4 Model of protruding stiffener in elastic plate -- 4.4.1 Introduction -- 4.4.2 Classical formulation -- 4.4.3 Zero-range potentials -- 4.4.4 Scattering by the zero-range potential -- 4.4.5 Choice of parameters in the model -- 4.4.6 Generalized model of protruding stiffener in fluid loaded plate -- Appendix A Regularization and Analysis of Boundary-Contact Integrals -- A.l Boundary-contact integrals in two dimensional problems -- A.2 Boundary-contact integrals for oblique incidence -- A.3 Low frequency asymptotics -- A.4 Boundary-contact integrals in three dimensions -- A.5 Boundary-contact integrals for the plate with infinite crack -- Appendix B Integral Equations of Convolution on a Finite Interval -- B.l Integral equations of convolution -- B.2 Logarithmic singularity of the kernel -- B.3 Supersingular kernels -- B.4 Smooth kernels -- Appendix C Models Used for Numerical Analysis -- Bibliography -- Index.