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Integral Transform Techniques for Green's Function

  • Book
  • © 2014

Overview

Authors:
  1. Kazumi Watanabe

    1. Dept. of Mechanical Engineering, Yamagata University, Yonezawa, Japan

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  • Reference book for engineers
  • Green's dyadics for elasto-dynamics problems in 2D and 3D are shown with their derivations
  • Cagniard's-de Hoop method is fully explained for 2D and 3D elasto-dynamic problems
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Applied and Computational Mechanics (LNACM, volume 71)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  2. Definition of Integral Transforms and Distributions

    • Kazumi Watanabe
    Pages 1-10

  3. Green’s Functions for Laplace and Wave Equations

    • Kazumi Watanabe
    Pages 11-42

  4. Green’s Dyadic for an Isotropic Elastic Solid

    • Kazumi Watanabe
    Pages 43-75

  5. Acoustic Wave in a Uniform Flow

    • Kazumi Watanabe
    Pages 77-92

  6. Green’s Functions for Beam and Plate

    • Kazumi Watanabe
    Pages 93-106

  7. Cagniard-de Hoop Technique

    • Kazumi Watanabe
    Pages 107-155

  8. Miscellaneous Green’s Functions

    • Kazumi Watanabe
    Pages 157-186

  9. Back Matter

    Pages 187-190
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Keywords

About this book

In this book mathematical techniques for integral transforms are described in detail but concisely. The techniques are applied to the standard partial differential equations, such as the Laplace equation, the wave equation and elasticity equations. The Green's functions for beams, plates and acoustic media are also shown along with their mathematical derivations. Lists of Green's functions are presented for the future use. The Cagniard's-de Hoop method for the double inversion is described in detail, and 2D and 3D elasto-dynamics problems are fully treated.

Authors and Affiliations

  • Dept. of Mechanical Engineering, Yamagata University, Yonezawa, Japan

    Kazumi Watanabe

About the author

Professor Watanabe is retired professor (2012) of mechanical engineering; he is active member of the advisory board of Acta Mechanica and has already co-edited a book at Springer

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