Modeling Surface Electrodes on a Piezoelectric Layer

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
B.-L. Wang ◽  
Y.-W. Mai
Keyword(s):  
Electric Field ◽  
Layer Thickness ◽  
Piezoelectric Layer ◽  
Electric Displacement ◽  
Closed Form Solution ◽  
Form Solution ◽  
Infinite Layer ◽  
Surface Electrodes ◽  
Electric Field Intensity Factor ◽  
Electromechanical Field

This paper considers a piezoelectric ceramic layer with a surface electrode. It focuses on the effect of the layer thickness on the electrode tip fields. A closed-form solution for the electromechanical fields at the electrode tip is obtained and is expressed in terms of the applied electric field intensity factor, which can be obtained exactly for infinite layer thickness and numerically for finite layer thickness. The stress, electric displacement, and electric field are plotted to show the effect of layer thickness. It is found that the stresses and field intensities at the electrode tip can be reduced considerably by decreasing the thickness of the piezoelectric layer, confirming the previous finding. The paper also gives a solution for two identical and collinear surface electrodes. The relative distance between the electrodes is observed to have significant influence on the electromechanical field in the piezoelectric layer.

scholarly journals Closed-form solution for piezoelectric layer with two collinear cracks parallel to the boundaries

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
B. M. Singh ◽  
J. Rokne ◽  
R. S. Dhaliwal
Keyword(s):  
Closed Form ◽  
Integral Equations ◽  
Piezoelectric Layer ◽  
Electric Displacement ◽  
Closed Form Solution ◽  
Finite Width ◽  
Intensity Factors ◽  
Collinear Cracks ◽  
Triple Integral Equations ◽  
Electromechanical Loading

We consider the problem of determining the stress distribution in an infinitely long piezoelectric layer of finite width, with two collinear cracks of equal length and parallel to the layer boundaries. Within the framework of reigning piezoelectric theory under mode III, the cracked piezoelectric layer subjected to combined electromechanical loading is analyzed. The faces of the layers are subjected to electromechanical loading. The collinear cracks are located at the middle plane of the layer parallel to its face. By the use of Fourier transforms we reduce the problem to solving a set of triple integral equations with cosine kernel and a weight function. The triple integral equations are solved exactly. Closed form analytical expressions for stress intensity factors, electric displacement intensity factors, and shape of crack and energy release rate are derived. As the limiting case, the solution of the problem with one crack in the layer is derived. Some numerical results for the physical quantities are obtained and displayed graphically.

scholarly journals Effect of Device Variables on Surface Potential and Threshold Voltage in DG-GNRFET

2015 ◽  
Vol 5 (5) ◽  
pp. 1003
Author(s):  
Baharak Mehrdel ◽  
Azlan Abdul Aziz ◽  
Mahdiar Hossein Ghadiri
Keyword(s):  
Electric Field ◽  
Surface Potential ◽  
Threshold Voltage ◽  
Structural Parameters ◽  
Closed Form Solution ◽  
Form Solution ◽  
Electric Field Effect ◽  
Short Channel ◽  
Lateral Electric Field ◽  
Saturation Velocity

<p><em>In this paper we present four simple analytical threshold voltage model for short- channel and length of saturation velocity region (LVSR) effect that takes into account the built – in potential of the source and drain channel junction, the surface potential and the surface electric field effect on double – gate graphene nanoribbon transistors. Four established models for surface potential, lateral electric field, LVSR and threshold voltage are presented. These models are based on the easy analytical solution of the two dimensional potential distribution in the graphene and Poisson equation which can be used to obtain surface potential, lateral electric field, LVSR and threshold voltage. These models give a closed form solution of the surface potential and electrical field distribution as a function of structural parameters and drain bias. Most of analytical outcomes are shown to correlate with outcomes acquired by Matlab simulation and the end model applicability to the published silicon base devices is demonstrated.</em></p>

scholarly journals Multiscale instabilities in soft heterogeneous dielectric elastomers

2014 ◽  
Vol 470 (2162) ◽  
pp. 20130618 ◽  
Author(s):  
S. Rudykh ◽  
K. Bhattacharya ◽  
G. deBotton
Keyword(s):  
Large Volume ◽  
Electric Displacement ◽  
Closed Form Solution ◽  
Form Solution ◽  
Dielectric Elastomers ◽  
Layered Composites ◽  
Volume Fractions ◽  
Moderate Volume ◽  
Layered Dielectrics ◽  
New Type

The development of instabilities in soft heterogeneous dielectric elastomers is investigated. Motivated by experiments and possible applications, we use in our analysis the physically relevant referential electric field instead of electric displacement. In terms of this variable, a closed form solution is derived for the class of layered neo-Hookean dielectrics. A criterion for the onset of electromechanical multiscale instabilities for the layered composites with anisotropic phases is formulated. A general condition for the onset of the macroscopic instability in soft multiphase dielectrics is introduced. In the example of the layered dielectrics, the essential influence of the microstructure on the onset of instabilities is revealed. We found that: (i)  macroscopic instabilities dominate at moderate volume fractions of the stiffer phase, (ii) interface instabilities appear at small volume fractions of the stiffer phase and (iii) instabilities of a finite scale, comparable to the microstructure size, occur at large volume fractions of the stiffer phase. The latest new type of instabilities does not appear in the purely mechanical case and dominates in the region of large volume fractions of the stiff phase.

A finite element multifrontal method for 3D CSEM modeling in the frequency domain

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. E101-E115 ◽  
Author(s):  
Nuno Vieira da Silva ◽  
Joanna V. Morgan ◽  
Lucy MacGregor ◽  
Mike Warner
Keyword(s):  
Finite Element ◽  
Electric Field ◽  
Frequency Domain ◽  
Closed Form Solution ◽  
Form Solution ◽  
Computational Domain ◽  
Order Partial Differential Equation ◽  
Primary Field ◽  
Direct Solver ◽  
Linear System Of Equations

There has been a recent increase in the use of controlled-source electromagnetic (CSEM) surveys in the exploration for oil and gas. We developed a modeling scheme for 3D CSEM modeling in the frequency domain. The electric field was decomposed in primary and secondary components to eliminate the singularity originated by the source term. The primary field was calculated using a closed form solution, and the secondary field was computed discretizing a second-order partial differential equation for the electric field with the edge finite element. The solution to the linear system of equations was obtained using a massive parallel multifrontal solver, because such solvers are robust for indefinite and ill-conditioned linear systems. Recent trends in parallel computing were investigated for their use in mitigating the computational overburden associated with the use of a direct solver, and of its feasibility for 3D CSEM forward modeling with the edge finite element. The computation of the primary field was parallelized, over the computational domain and the number of sources, using a hybrid model of parallelism. When using a direct solver, the attainment of multisource solutions was only competitive if the same factors are used to achieve a solution for multi right-hand sides. This aspect was also investigated using the presented methodology. We tested our proposed approach using 1D and 3D synthetic models, and they demonstrated that it is robust and suitable for 3D CSEM modeling using a distributed memory system. The codes could thus be used to help design new surveys, as well to estimate subsurface conductivities through the implementation of an appropriate inversion scheme.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

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