scholarly journals Propagators from integral representations of Green’s functions for the N‐dimensional free‐particle, harmonic oscillator and Coulomb problems

1984 ◽  
Vol 25 (4) ◽  
pp. 905-909 ◽  
Author(s):  
S. M. Blinder
Keyword(s):  
Harmonic Oscillator ◽  
Green's Functions ◽  
Green’S Functions ◽  
Free Particle ◽  
Integral Representations

Analysis of Spatial Steady-State Vibrations of a Layered Anisotropic Plate Using the Green’s Functions

2010 ◽  
Author(s):  
Alexander Karmazin ◽  
Evgenia Kirillova ◽  
Wolfgang Seemann ◽  
Pavel Syromyatnikov
Keyword(s):  
Fourier Transform ◽  
Steady State ◽  
Green's Functions ◽  
Anisotropic Plate ◽  
Fourier Transforms ◽  
Green’S Functions ◽  
Displacement Vector ◽  
Integral Representations ◽  
Surface Load ◽  
The Real

Spatial steady-state harmonic vibrations of a layered anisotropic plate excited by the distributed sources are considered. The work is based on the classical methods of the integral Fourier transforms and integral representations of the Green’s functions. In Fourier transform domain, the displacement vector is represented in terms of the Green’s matrix transform and the transform of the surface load vector. The two-dimensional inverse Fourier transform of the displacement vector is computed by reducing double integral to the iterated one with integrating along a contour, which deviates from the real axis while bypassing the real poles, and with subsequent integrating along the wave propagation angle. Three numerical algorithms of computing related iterated integrals are presented. The features of the application of these algorithms for the near- and far-field zones of the source are discussed. All of presented methods are compared for the numerical examples of vibrations on the surface of 24-layer symmetrical composite.

scholarly journals Green's functions for the wave, Helmholtz and Poisson equations in a two-dimensional boundless domain

2013 ◽  
Vol 35 (1) ◽  
Author(s):  
Roberto Toscano Couto
Keyword(s):  
Green's Functions ◽  
Fourier Transforms ◽  
Green’S Functions ◽  
Plane Domain ◽  
Integral Representations ◽  
Two Dimensional ◽  
Entire Plane ◽  
Poisson Equations ◽  
New Procedures ◽  
Real Poles

In this work, Green's functions for the two-dimensional wave, Helmholtz and Poisson equations are calculated in the entire plane domain by means of the two-dimensional Fourier transform. New procedures are provided for the evaluation of the improper double integrals related to the inverse Fourier transforms that furnish these Green's functions. The integrals are calculated by using contour integration in the complex plane. The method consists basically in applying the correct prescription for circumventing the real poles of the integrand as well as in using well-known integral representations of some Bessel functions.

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