1.

Record Nr.

UNINA9910784515103321

Autore

Andronov I. V (Ivan V.)

Titolo

Generalized point models in structural mechanics [[electronic resource] /] / Ivan V. Andronov

Pubbl/distr/stampa

Singapore ; ; River Edge, N.J., : World Scientific, c2002

ISBN

981-277-790-3

Descrizione fisica

1 online resource (276 p.)

Collana

Series on stability, vibration, and control of systems. Series A ; ; v. 5

Disciplina

515.35

624.1/71

624.171

Soggetti

Structural analysis (Engineering) - Mathematical models

Structural engineering

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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

Sommario/riassunto

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><