Integral Transform Techniques for Green's Function

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.

List of contents

Definition of integral transforms and distributions.- Green's functions for Laplace and wave equations.- Green's dyadic for an isotropic elastic solid.- Acoustic wave in an uniform flow.- Green's functions for beam and plate.- Cagniard de Hoop technique.- Miscellaneous Green's functions.- Exercises.

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

Summary

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.

Product details

• Authors: Kazumi Watanabe
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.01.2015
• EAN: 9783319174549
• ISBN: 978-3-31-917454-9
• No. of pages: 264
• Dimensions: 172 mm x 19 mm x 243 mm
• Weight: 532 g
• Illustrations: XIV, 264 p. 53 illus., 26 illus. in color.
• Series: Lecture Notes in Applied and Computational Mechanics; Lecture Notes in Applied and Computational Mechanics
• Subjects: Natural sciences, medicine, IT, technology > Technology > General, dictionaries; B, engineering, Civil Engineering, Mathematical and Computational Engineering, Theoretical and Applied Mechanics, Mechanics, Mechanics of solids, Mechanics, Applied, Engineering mathematics, Applied mathematics, Mathematical and Computational Engineering Applications, Operational calculus, Integral transforms, Integral Transforms and Operational Calculus, Integral Transforms, Operational Calculus, Integral calculus & equations