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Stationary Oscillations of Elastic Plates: A Boundary Integral Equation Analysis
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Catalogue Record 28049
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Catalogue Information
Nome campo
dettagli
Dewey Class
515.45
Titolo
Stationary Oscillations of Elastic Plates ([Ebook]) : A Boundary Integral Equation Analysis / by Gavin R. Thomson, Christian Constanda.
Autore
Thomson, Gavin R.
Added Personal Name
Constanda, Christian
Other name(s)
SpringerLink (Online service)
Pubblicazione
Boston : Birkhäuser , 2011.
Physical Details
XIII, 230 pages, 4 illus. : online resource.
ISBN
9780817682415
Summary Note
Elliptic partial differential equations are important for approaching many problems in mathematical physics, and boundary integral methods play a significant role in their solution. This monograph investigates the latter as they arise in the theory characterizing stationary vibrations of thin elastic plates. The techniques used reduce the complexity of classical three-dimensional elasticity to a system of two independent variables, using eigenfrequencies to model problems with flexural-vibrational elastic body deformation and simplifying these problems to manageable, uniquely solvable integral equations. In under 250 pages, Stationary Oscillations of Elastic Plates develops an impressive amount of theoretical machinery. After introducing the equations describing the vibrations of elastic plates in the first chapter, the book proceeds to explore topics including the single-layer and double-layer plate potentials; the Newtonian potential; the exterior boundary value problems; the direct boundary integral equation method; the Robin boundary value problems; the boundary-contact problem; the null field equations. Throughout, ample time is allotted to laying the groundwork necessary for establishing the existence and uniqueness of solutions to the problems discussed. The book is meant for readers with a knowledge of advanced calculus and some familiarity with functional analysis. It is a useful tool for professionals in pure and applied mathematicians, as well as for theoretical physicists and mechanical engineers with practices involving elastic plates. Graduate students in these fields would also benefit from the monograph as a supplementary text for courses relating to theories of elasticity or flexural vibrations.:
Contents note
Preface -- The Mathematical Models -- Layer Potentials -- The Nonhomogenous System -- The Question of Uniqueness for the Exterior Problems -- The Eigenfrequency Spectra of the Interior Problems -- The Question of Solvability -- The Direct Boundary Equation Formulation -- Modified Fundamental Solutions -- Problems with Robin Boundary Conditions -- The Transmission Problem -- The Null Field Equations -- Appendices -- References -- Index.
System details note
Online access is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-0-8176-8241-5
Link alle Opere Legate
Riferimenti soggetto:
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Differential equations, Partial
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Integral Equations
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Mathematical Methods in Physics
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Mathematical Physics
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Mathematics
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Partial differential equations
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Vibration
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Vibration, Dynamical Systems, Control
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Authors:
author
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Constanda, Christian
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Thomson, Gavin R.
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Corporate Authors:
SpringerLink (Online service)
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Classification:
515.45
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