A new computational algorithm for Green's functions: Fourier transform of the Newton polynomial expansion

By choosing appropriate paths of integration in both the complex frequency ω and complex wavenumber k planes, exact Green’s functions for elastic wave propagation in axisymmetric fluid‐filled boreholes in solid elastic media are expressed completely as sums of modes. There are no contributions from branch line integrals. The integrations with respect to k are performed exactly using Cauchy residue theory. The remaining integrations with respect to ω are then carried out partly by using the fast Fourier transform (FFT) and partly by using another numerical method. Provided that the number of points in the FFT can be taken sufficiently large, there are no restrictions on distance. The method is fast, accurate, and easy to apply.

Download Full-text

Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations

Handbook of Materials Modeling ◽

10.1007/978-3-319-44677-6_15 ◽

2020 ◽

pp. 1657-1683

Author(s):

Ricardo A. Lebensohn

Keyword(s):

Fourier Transform ◽

Fast Fourier Transform ◽

Green's Functions ◽

Green’S Functions ◽

Mean Field ◽

Full Field ◽

Polycrystal Plasticity ◽

Self Consistent

Download Full-text

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

ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Volume 2 ◽

10.1115/esda2010-25430 ◽

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.

Download Full-text

Numerical evaluation of Green’s functions for axisymmetric boreholes using leaking modes

Geophysics ◽

10.1190/1.1442375 ◽

1987 ◽

Vol 52 (8) ◽

pp. 1099-1105 ◽

Cited By ~ 6

Author(s):

R. A. W. Haddon

Keyword(s):

Wave Propagation ◽

Fourier Transform ◽

Elastic Wave ◽

Numerical Evaluation ◽

Green's Functions ◽

Green’S Functions ◽

Complete Solution ◽

Body Waves ◽

Complex Frequency ◽

Residue Theory

By choosing appropriate paths of integration in both the complex frequency (ω) and complex wavenumber (k) planes, exact Green’s functions for elastic wave propagation in axisymmetric boreholes are expressed completely as sums of modes. The integrations with respect to k are performed exactly using Cauchy residue theory. The remaining integrations with respect to ω are then carried out using the fast Fourier transform (FFT). The complete solution, including all possible body waves, is expressed simply as a superposition of modes without any contributions from branch line integrals. There are no spurious arrivals and, provided that the number of points in the FFT can be taken sufficiently large, no restrictions on distance. The method is fast, accurate, and easy to apply.

Download Full-text