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Integral Transform Techniques for Green's Function

  • Kazumi Watanabe

Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 76)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Kazumi Watanabe
    Pages 121-137
  3. Kazumi Watanabe
    Pages 139-152
  4. Kazumi Watanabe
    Pages 153-204
  5. Kazumi Watanabe
    Pages 205-260
  6. Back Matter
    Pages 261-264

About this book

Introduction

This book describes mathematical techniques for integral transforms in a detailed but concise manner. The techniques are subsequently applied to the standard partial differential equations, such as the Laplace equation, the wave equation and elasticity equations. Green’s functions for beams, plates and acoustic media are also shown, along with their mathematical derivations. The Cagniard-de Hoop method for double inversion is described in detail, and 2D and 3D elastodynamic problems are treated in full.

This new edition explains in detail how to introduce the branch cut for the multi-valued square root function. Further, an exact closed form Green’s function for torsional waves is presented, as well as an application technique of the complex integral, which includes the square root function and an application technique of the complex integral.

Keywords

Cagniard's-de Hoop Techniques Exact Solutions Green's Function and Dyadic Integral Transform Wave Phenomena

Authors and affiliations

  • Kazumi Watanabe
    • 1
  1. 1.Yamagata UniversityYonezawaJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-17455-6
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-17454-9
  • Online ISBN 978-3-319-17455-6
  • Series Print ISSN 1613-7736
  • Series Online ISSN 1860-0816
  • Buy this book on publisher's site