Generalized point models in structural mechanics
Ivan V. Andronov.
Bok Engelsk 2002 I. V. Andronov,· Electronic books.
| Utgitt | Singapore ; River Edge, N.J. : : World Scientific, , c2002.
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| Omfang | 1 online resource (276 p.)
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| Opplysninger | Description based upon print version of record.. - 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. - This book presents the idea of zero-range potentials and shows the limitations of the point models used in structural mechanics. It also offers specific examples from the theory of generalized functions, regularization of super-singular integral equations and other specifics of the boundary value problems for partial differential operators of the fourth order. <br><i>Contents:</i><ul><li>Vibrations of Thin Elastic Plates and Classical Point Models</li><li>Operator Methods in Diffraction</li><li>Generalized Point Models</li><li>Discussions and Recommendations for Future Research</li></ul><br><
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| ISBN | 9810248784
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