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Cubierta del libro
Autor Thomson, Gavin R. author.

Título Stationary Oscillations of Elastic Plates [electronic resource] : A Boundary Integral Equation Analysis / by Gavin R. Thomson, Christian Constanda.

Publicación Boston : Birkhäuser Boston, 2011.
Descripción física XIII, 230 p. 4 illus. online resource.
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Colección Springer eBooks. Mathematics and Statistics
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Contiene: 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.
Resumen: 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.
Materia Mathematics.
Integral equations.
Partial differential equations.
Dynamical systems.
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Integral Equations.
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Vibration, Dynamical Systems, Control.
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Mathematical Methods in Physics.
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Partial Differential Equations.
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Autor secundario Constanda, Christian., author.
SpringerLink (Online service)
En Springer eBooks
OTRO SOPORTE Printed edition: 9780817682408
ISBN 9780817682415 978-0-8176-8241-5
ISBN/ISSN 10.1007/978-0-8176-8241-5 doi