Stationary Oscillations of Elastic Plates

A Boundary Integral Equation Analysis

  • Gavin R. Thomson
  • Christian Constanda

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Gavin R. Thomson, Christian Constanda
    Pages 1-5
  3. Gavin R. Thomson, Christian Constanda
    Pages 7-22
  4. Gavin R. Thomson, Christian Constanda
    Pages 23-46
  5. Gavin R. Thomson, Christian Constanda
    Pages 47-59
  6. Gavin R. Thomson, Christian Constanda
    Pages 61-74
  7. Gavin R. Thomson, Christian Constanda
    Pages 75-86
  8. Gavin R. Thomson, Christian Constanda
    Pages 87-102
  9. Gavin R. Thomson, Christian Constanda
    Pages 103-152
  10. Gavin R. Thomson, Christian Constanda
    Pages 153-175
  11. Gavin R. Thomson, Christian Constanda
    Pages 177-190
  12. Gavin R. Thomson, Christian Constanda
    Pages 191-204
  13. Back Matter
    Pages 205-230

About this book

Introduction

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.

Keywords

boundary integral equations elastic plates elliptic partial differential equations potential methods stationary oscillation

Authors and affiliations

  • Gavin R. Thomson
    • 1
  • Christian Constanda
    • 2
  1. 1.A.C.C.A.GlasgowUnited Kingdom
  2. 2., Department of Mathematical and ComputerThe University of TulsaTulsaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8241-5
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8240-8
  • Online ISBN 978-0-8176-8241-5
  • About this book