Interior Green's Function Solution for a Thick and Finite Dielectric Slab

2007 ◽  
Vol 55 (12) ◽  
pp. 3504-3514 ◽  
Author(s):  
Armin Parsa ◽  
Robert Paknys
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Dielectric Slab ◽  
Function Solution

scholarly journals Method of Moment Analysis of Carbon Nanotubes Embedded in A Lossy Dielectric Slab Using A Multilayer Dyadic Green’s Function

2021 ◽  
Author(s):  
SUMITRA DEY ◽  
Deb chatterjee ◽  
Edward Garboczi ◽  
Ahmed M. Hassan
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Dielectric Slab ◽  
Method Of Moment ◽  
Dyadic Green’S Function ◽  
Dyadic Green's Function ◽  
Aspect Ratios ◽  
Wide Range ◽  
Speed Up ◽  
Lossy Dielectric

<div>Modeling the electromagnetic response of carbon nanotube (CNT) reinforced composites is inherently a three dimensional (3D) multi-scale problem that is challenging to solve in real-time for nondestructive evaluation applications. This article presents a fast and accurate full-wave electromagnetic solver based on a multi-layer dyadic Green’s function approach. In this approach, we account for the effects of the dielectric slab, where the CNTs are embedded, without explicitly discretizing its interfaces. Due to their large aspect ratios, the CNTs are modeled as arbitrary thin wires (ATWs), and the method of moment (MoM) formulation with distributed line impedance is used to solve for their coupled currents. The accuracy of the inhouse solver is validated against commercial method of moment (MoM) and finite element method (FEM) solvers over a broad range of frequencies (from 1 GHz to 10 THz) and for a wide range of dielectric slab properties. Examples of 100nm long vertical and horizontal CNTs embedded in a 1 μm thick lossy dielectric substrate are presented. The in-house solver provides more than 50 ✕ speed up while solving the vertical CNT, and more than 570 ✕ speed up while solving the horizontal CNT than a commercial MoM solver over the GHz to THz frequency range.</div>

A method for the coupled field of an orthotropic piezoelectric plate subjected to an arbitrary electro-mechanical load

2020 ◽  
Vol 25 (11) ◽  
pp. 2132-2152
Author(s):  
ShouMing Shang ◽  
PengFei Hou ◽  
J Tong
Keyword(s):  
General Solution ◽  
Green’S Function ◽  
Green's Function ◽  
Mechanical Load ◽  
Piezoelectric Plate ◽  
Numerical Results ◽  
Function Solution ◽  
Coupled Field ◽  
Piezoelectric Devices ◽  
Plate Type

There are a number of plate-type piezoelectric devices in engineering, hence it is crucial to search for a method that can accurately acquire the electro-mechanical coupled field of a piezoelectric plate. A method for calculating the coupled field of an orthotropic piezoelectric plate with arbitrary thickness under an arbitrary electro-mechanical load is put forward in this article. First, the Green’s function solution of an orthotropic piezoelectric plate subjected to a line charge and a normal line force is derived based on the general solution of the orthotropic piezoelectric material. All stress and electric components of the orthotropic piezoelectric plate are derived when the general solution is substituted into suitable harmonic functions containing undetermined constants. Once the boundary conditions and electro-mechanical equilibrium conditions are satisfied, those constants can be solved. In addition, according to the obtained Green’s function solution and superposition principle, the coupled field of the orthotropic piezoelectric plate subjected to an arbitrary electro-mechanical load can be solved. Numerical results indicate that the convergence and precision of the method are quite good. A concise skill without repeated calculations is also presented for acquiring the coupled fields in the orthotropic piezoelectric plates with various thickness, which facilitates the effective design of plate thickness in plate-type piezoelectric devices. Finally, some valuable conclusions for the fine design of plate-type piezoelectric sensors, energy harvesters and actuators are presented based on the numerical results.

Green’s Functions for Two-Phase Transversely Isotropic Materials

1979 ◽  
Vol 46 (3) ◽  
pp. 551-556 ◽  
Author(s):  
Y.-C. Pan ◽  
T.-W. Chou
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Elastic Constants ◽  
Transversely Isotropic ◽  
Two Phase ◽  
Closed Form Solutions ◽  
Isotropic Materials ◽  
Function Solution ◽  
Present Solution ◽  
Plane Of Isotropy

Closed-form solutions are obtained for the Green’s function problems of point forces applied in the interior of a two-phase material consisting of two semi-infinite transversely isotropic elastic media bonded along a plane interface. The interface is parallel to the plane of isotropy of both media. The solutions are applicable to all combinations of elastic constants. The present solution reduces to Sueklo’s expression when the point force is normal to the plane of isotropy and (C11C33)1/2 ≠ C13 + 2C44 for both phases. When the elastic constants of one of the phases are set to zero, the solution can be reduced to the Green’s function for semi-infinite media obtained by Michell, Lekhnitzki, Hu, Shield, and Pan and Chou. The Green’s function solution of Pan and Chou for an infinite transversely isotropic solid can be reproduced from the present expression by setting the elastic constants of both phases to be equal. Finally, the Green’s function for isotropic materials can also be obtained from the present solution by suitable substitution of elastic constants.

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