05231nam 2200661Ia 450 991078451510332120230607221408.0981-277-790-3(CKB)1000000000399395(EBL)1679609(OCoLC)879074270(SSID)ssj0000161442(PQKBManifestationID)11177598(PQKBTitleCode)TC0000161442(PQKBWorkID)10198513(PQKB)10058661(MiAaPQ)EBC1679609(WSP)00004901(Au-PeEL)EBL1679609(CaPaEBR)ebr10201158(CaONFJC)MIL505425(EXLCZ)99100000000039939520020729d2002 uy 0engur|n|---|||||txtccrGeneralized point models in structural mechanics[electronic resource] /Ivan V. AndronovSingapore ;River Edge, N.J. World Scientificc20021 online resource (276 p.)Series on stability, vibration, and control of systems. Series A ;v. 5Description based upon print version of record.981-02-4878-4 Includes bibliographical references and index.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 conditions1.1.4 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 solution1.3.6 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 crack1.5.1 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 Operators2.1.3 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 operator2.3.2 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><Series on stability, vibration, and control of systems.Series A ;v. 5.Structural analysis (Engineering)Mathematical modelsStructural engineeringStructural analysis (Engineering)Mathematical models.Structural engineering.515.35624.1/71624.171Andronov I. V(Ivan V.)1126698MiAaPQMiAaPQMiAaPQBOOK9910784515103321Generalized point models in structural mechanics3829564UNINA