rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Stationary Oscillations of Elastic Plates
    sub title: A Boundary Integral Equation Analysis
  name:
    name part: Thomson, Gavin R.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Constanda, Christian.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 230 p. 4 illus. online resource.
  abstract: 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.
  table of contents: 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.
  note: by Gavin R. Thomson, Christian Constanda.
  subject:
    topic: Mathematics
  subject:
    topic: Integral equations
  subject:
    topic: Partial differential equations
  subject:
    topic: Physics
  subject:
    topic: Vibration
  subject:
    topic: Dynamical systems
  subject:
    topic: Dynamics
  subject:
    topic: Mathematics
  subject:
    topic: Integral Equations
  subject:
    topic: Vibration, Dynamical Systems, Control
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Partial Differential Equations
  classification: QA431
  classification: 515.45
  related item:
    title info:
      title: Springer eBooks
  identifier: 9780817682415
  identifier: http://dx.doi.org/10.1007/978-0-8176-8241-5
  record info:
    record creation date: 110627
    record change date: 20151125193323.0
    record identifier: 978-0-8176-8241-5