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Integral Transform Techniques for Green's Function [electronic resource] / by Kazumi Watanabe.

By: Watanabe, Kazumi [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Applied and Computational Mechanics: 76Publisher: Cham : Springer International Publishing : Imprint: Springer, 2015Edition: 2nd ed. 2015.Description: XIV, 264 p. 53 illus., 26 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319174556.Subject(s): Engineering | Integral transforms | Operational calculus | Applied mathematics | Engineering mathematics | Mechanics | Mechanics, Applied | Engineering | Appl.Mathematics/Computational Methods of Engineering | Theoretical and Applied Mechanics | Integral Transforms, Operational CalculusAdditional physical formats: Printed edition:: No titleDDC classification: 519 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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