Titlebook: Integral Transform Techniques for Green‘s Function; Kazumi Watanabe Book 2015Latest edition Springer International Publishing Switzerland

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Kazumi WatanabeA valuable reference book for engineers.Includes full descriptions of the Cagniard-de Hoop technique and the branch cut for square root functions.Employs a unified mathematical technique as the soluti

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https://doi.org/10.1007/978-3-319-17455-6Cagniard‘s-de Hoop Techniques; Exact Solutions; Green‘s Function and Dyadic; Integral Transform; Wave Ph

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,Green’s Dyadic for an Isotropic Elastic Solid,onses, are obtained by the integral transform method. The time-harmonic response is derived by the convolution integral of the impulsive response without solving the differential equations for the time-harmonic source. In the last section, two exact closed form Green‘s functions for torsional waves are also presented.

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Definition of Integral Transforms and Distributions,unctions which are frequently used as the source function, and a concise introduction of the branch cut for a multi-valued square root function. The multiple integral transforms and their notations are also explained. The newly added Sect. 1.3 explains closely how to introduce the branch cut for the

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,Green’s Functions for Laplace and Wave Equations,ique of the integral transform method is demonstrated. Especially, in the case of the time-harmonic response for the 1 and 2D wave equations, the integration path for the inversion integral is discussed in detail with use of the results in Sect. 1.3. At the end of the chapter, the obtained Green‘s f

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,Green’s Functions for Beam and Plate,eam and plate are discussed. Two dynamic responses, the impulsive and time-harmonic responses, are derived by the integral transform method. In addition to the tabulated integration formulas, an inversion integral is evaluated by the application of the complex integral theory.