Integral Transform Techniques for Green's Function [electronic resource] / by Kazumi Watanabe.Material type: TextLanguage: English Series: Lecture Notes in Applied and Computational Mechanics: 71Publisher: Cham : Springer International Publishing : Imprint: Springer, 2014Description: XII, 190 p. 34 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319008790Subject(s): Engineering | Integral Transforms | Engineering mathematics | 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 LOC classification: TA329-348TA640-643Online resources: Click here to access online
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 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.