scholarly journals Efficient Computation of the Green’s Function and Its Derivatives for Three-Dimensional Piezoelectricity

2019 ◽  
Vol 22 (1) ◽  
pp. 104-104
Author(s):  
Cristiano Ubessi ◽  
Federico C. Buroni ◽  
Gabriel Hattori ◽  
Andr閟 S醗z ◽  
Rog閞io J. Marczak
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Three Dimensional ◽  
Efficient Computation

scholarly journals A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method

2021 ◽  
Vol 11 (6) ◽  
pp. 2722
Author(s):  
Zhiwen Qian ◽  
Dejiang Shang ◽  
Yuan Hu ◽  
Xinyang Xu ◽  
Haihan Zhao ◽  
...  
Keyword(s):  
Green’S Function ◽  
Shallow Water ◽  
Green's Function ◽  
Plane Waves ◽  
Spherical Wave ◽  
Sound Field ◽  
Efficient Computation ◽  
Image Source ◽  
Source Method ◽  
Pekeris Waveguide

The Green’s function (GF) directly eases the efficient computation for acoustic radiation problems in shallow water with the use of the Helmholtz integral equation. The difficulty in solving the GF in shallow water lies in the need to consider the boundary effects. In this paper, a rigorous theoretical model of interactions between the spherical wave and the liquid boundary is established by Fourier transform. The accurate and adaptive GF for the acoustic problems in the Pekeris waveguide with lossy seabed is derived, which is based on the image source method (ISM) and wave acoustics. First, the spherical wave is decomposed into plane waves in different incident angles. Second, each plane wave is multiplied by the corresponding reflection coefficient to obtain the reflected sound field, and the field is superposed to obtain the reflected sound field of the spherical wave. Then, the sound field of all image sources and the physical source are summed to obtain the GF in the Pekeris waveguide. The results computed by this method are compared with the standard wavenumber integration method, which verifies the accuracy of the GF for the near- and far-field acoustic problems. The influence of seabed attenuation on modal interference patterns is analyzed.

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

Formulation of Three-Dimensional Green’s Function and its Application to Fatigue Life Evaluation of Pressurizer

2006 ◽  
Vol 324-325 ◽  
pp. 387-390
Author(s):  
Yoon Suk Chang ◽  
Shin Beom Choi ◽  
Jae Boong Choi ◽  
Young Jin Kim ◽  
Myung Jo Jhung ◽  
...  
Keyword(s):  
Finite Element ◽  
Fatigue Life ◽  
Green’S Function ◽  
Green's Function ◽  
Three Dimensional ◽  
Stress Transfer ◽  
Life Assessment ◽  
Element Analysis ◽  
Fatigue Evaluation ◽  
Effective Assessment

Major nuclear components have been designed by conservative codes to prevent unanticipated fatigue failure. However, more realistic and effective assessment is necessary in proof of continued operation beyond the design life. In the present paper, three-dimensional stress and fatigue evaluation is carried out for pressurizer employing complex full geometry itself instead of conventional discrete subcomponents. For this purpose, temperature and mechanical stress transfer Green’s functions are derived from finite element analyses and applied to critical locations of pressurizer. In accordance with comparison of resulting stresses obtained from the Green’s function and detailed finite element analysis, suitability of the specific Green’s function is investigated. Finally, prototype of fatigue life assessment results is provided along with relevant ongoing activities.

Green’s function–based surrogate model for windfields using limited samples

2017 ◽  
Vol 42 (3) ◽  
pp. 164-176 ◽  
Author(s):  
Joshua Paul Marshall ◽  
Joseph David Richardson ◽  
Carlos Jose Montalvo
Keyword(s):  
Green’S Function ◽  
Wind Velocity ◽  
Green's Function ◽  
Surrogate Model ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Fast Method ◽  
Three Dimensional Model ◽  
Wind Velocities ◽  
Wind Measurements

There exists many applications for which wind-velocity is desired over a three-dimensional space. The vector field associated with these wind velocities is known as a “windfield” or “velocity-windfield.” The present work provides a fast method to characterize windfields. The approach uses the free-space Green’s function for potential theory as an inexpensive surrogate model in lieu of either complicated physics-based models or other types of surrogate models, both of which require volumetric discretizations for the three-dimensional case. Using the gradient of the third Green’s identity, the wind-velocity in the interior of a domain is entirely characterized by a surface discretization while still providing a three-dimensional model. The unknown densities on the surface are determined from enforcement of the interior form of the identity at arbitrary points coinciding with wind measurements taken by unmanned aerial vehicles. Numerical results support the feasibility of the method.

scholarly journals THE MOTIONS OF A MOORED SHIP IN A HARBOR BASIN

1982 ◽  
Vol 1 (18) ◽  
pp. 165 ◽  
Author(s):  
T. Sawaragi ◽  
M. Kubo
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Close Agreement ◽  
Three Dimensional ◽  
Ship Motion ◽  
Experimental Results ◽  
New Methods

In harbors affected by ocean swells,cargo handlings are often interrupted and irooring lines are broken as a result of severe ship motionsl). In order to decrease such accidents, the noored ship notions in a harbor basin must be studied. In this paper the ship notions in the harbor basin are investigated by using three dimensional Green's function and close agreement between theoretical and experimental results can be found. New methods to reduce noored ship motion are also proposed. The efficiency of these methods is verified theoretically and experimentally.

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