Effective Behavior of Piezoelectric Composites

1994 ◽  
Vol 47 (1S) ◽  
pp. S112-S121 ◽  
Author(s):  
Biao Wang
Keyword(s):  
Electric Field ◽  
Piezoelectric Material ◽  
Transversely Isotropic ◽  
Piezoelectric Composite ◽  
Algebraic Equations ◽  
Piezoelectric Composites ◽  
Spheroidal Inclusion ◽  
Linear Algebraic Equations ◽  
General Relations ◽  
Effective Constants

In this paper, general relations between the overall properties of piezoelectric composites and the properties of their constituents are derived. Based on the solution for an ellipsoidal inclusion in a piezoelectric material developed by Wang (Int. J. Solids and Structures, 29, 293, 1992), it is found that the coupled elastic and electric field inside a spheroidal inclusion in a transversely isotropic, piezoelectric matrix can be expressed in terms of a system of the linear algebraic equations which contains only some simple integrals. These internal fields are then used to obtain the effective constants of a piezoelectric composite.

Exact results in the micromechanics of fibrous piezoelectric composites exhibiting pyroelectricity

1993 ◽  
Vol 441 (1911) ◽  
pp. 59-81 ◽  
Keyword(s):  
Transversely Isotropic ◽  
Dielectric Constants ◽  
Local Fields ◽  
Piezoelectric Composite ◽  
Uniform Temperature ◽  
Piezoelectric Composites ◽  
Three Phase ◽  
Phase Systems ◽  
Electromechanical Loading ◽  
Exact Relations

Piezoelectric fibrous composites of two, three and four phases are considered. The phase boundaries are cylindrical but otherwise the microgeometry is totally arbitrary. The constituents are transversely isotropic, and exhibit pyroelectricity. Exact relations are derived between the local fields arising under a uniform electromechanical loading and a uniform temperature change in the piezoelectric composite. For given overall material symmetry, exact connections are obtained among the effective elastic, piezoelectric and dielectric constants of two- and three- phase systems. It is also shown that the effective thermal stress and pyroelectric coefficients can be expressed in terms of the effective elastic, piezoelectric, dielectric constants and constituent properties in two-, three- and four-phase composites.

Modeling and Analysis of 1-3 Piezoelectric Composites

2002 ◽  
Author(s):  
Sanjay Nakhwa ◽  
Anil Saigal
Keyword(s):  
Boundary Conditions ◽  
Material Properties ◽  
Volume Fraction ◽  
Transversely Isotropic ◽  
Unit Cell ◽  
Coupling Constants ◽  
Upper And Lower Bounds ◽  
Piezoelectric Composite ◽  
Piezoelectric Composites ◽  
Material Constants

Theoretical results of the material properties of piezoelectric composites are generally limited to the transversely isotropic composites and are usually given in the form of upper and lower bounds. In most of these analyses all the material constants cannot be determined. However, the method of effective field has been used on a transversely isotropic piezoelectric composite to theoretically calculate all the ten material properties. In this work an alternative method to determine all the elastic, dielectric and piezoelectric coupling constants of 1-3 piezoelectric composite with periodic arrangement of fibers are investigated by using finite element analysis on a unit cell model. FEA of unit cell models for hexagonal, square with diagonal and square with edge orientation topologies are performed. Different mechanical and electrical loading patterns and their corresponding boundary conditions are formulated and simulated to get data necessary for deriving the various anisotropic material constants. FEA results are compared with those of the theoretical work. Effect of different parameters e.g. volume fraction, topology and electrical boundary conditions on the different material constants are discussed.

Asymptotic Behavior of the Solution to the Axisymmetric Dynamical Problem of the Elasticity Theory for the Transversally Isotropic Spherical Layer of Small Thickness

2020 ◽  
pp. 61-71
Author(s):  
M.F. Mehdiyev ◽  
N.K. Akhmedov ◽  
S.M. Yusubova
Keyword(s):  
Dynamic Problem ◽  
Transversely Isotropic ◽  
Spherical Layer ◽  
Theory Of Elasticity ◽  
Dynamical Problem ◽  
Algebraic Equations ◽  
Elastic Band ◽  
Small Thickness ◽  
Homogeneous Solutions ◽  
Linear Algebraic Equations

In this paper, we study the axisymmetric dynamic problem of the theory of elasticity for the transversely isotropic spherical layer of small thickness that does not contain any of the poles 0 and π. It is assumed that the lateral surface of the sphere is free of stresses, and boundary conditions are set on conical sections. Using the method of asymptotic integration of equations of the theory of elasticity, the dynamic problem of this theory is analyzed for the transversely isotropic spherical layer as the thin-walled parameter tends to zero. A possible form of wave formation in the transversely isotropic spherical layer has been studied depending on the frequency of the influencing forces. Homogeneous solutions are constructed and their classification is given. Asymptotic expansions of the homogeneous solutions are obtained, which make possible to calculate the stress-strain state for various values of the frequency of the influencing forces. It is shown that for the high-frequency oscillations in the first term of the asymptotics, the dispersion equation coincides with the well-known Rayleigh-Lamb equation for the elastic band. In the general case of loading on the sphere using the Hamilton variational principle, the boundary-value problem is reduced to the solving infinite systems of linear algebraic equations.

scholarly journals Simulation of microwave circuits and laser structures including PML by means of FIT

2005 ◽  
Vol 2 ◽  
pp. 107-112
Author(s):  
G. Hebermehl ◽  
J. Schefter ◽  
R. Schlundt ◽  
Th. Tischler ◽  
H. Zscheile ◽  
...  
Keyword(s):  
Electric Field ◽  
Boundary Value Problem ◽  
Large Scale ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Microwave Circuits ◽  
Algebraic Equations ◽  
Fine Grid ◽  
Preconditioning Techniques ◽  
Linear Algebraic Equations

Abstract. Field-oriented methods which describe the physical properties of microwave circuits and optical structures are an indispensable tool to avoid costly and time-consuming redesign cycles. Commonly the electromagnetic characteristics of the structures are described by the scattering matrix which is extracted from the orthogonal decomposition of the electric field. The electric field is the solution of an eigenvalue and a boundary value problem for Maxwell’s equations in the frequency domain. We discretize the equations with staggered orthogonal grids using the Finite Integration Technique (FIT). Maxwellian grid equations are formulated for staggered nonequidistant rectangular grids and for tetrahedral nets with corresponding dual Voronoi cells. The interesting modes of smallest attenuation are found solving a sequence of eigenvalue problems of modified matrices. To reduce the execution time for high-dimensional problems a coarse and a fine grid is used. The calculations are carried out, using two levels of parallelization. The discretized boundary value problem, a large-scale system of linear algebraic equations with different right-hand sides, is solved by a block Krylov subspace method with various preconditioning techniques. Special attention is paid to the Perfectly Matched Layer boundary condition (PML) which causes non physical modes and a significantly increased number of iterations in the iterative methods.

Stress Distribution in a Piezoelectric Material with an Elliptical Hole Subjected to Remote Uniform Shear Mechanical and Electric Loads

2010 ◽  
Vol 97-101 ◽  
pp. 956-959
Author(s):  
Min Juan Zhou ◽  
Shi Jie Duan ◽  
Yan Ping Kong ◽  
Shu Hong Liu
Keyword(s):  
Electric Field ◽  
Piezoelectric Material ◽  
Elliptical Hole ◽  
Transversely Isotropic ◽  
Shielding Effect ◽  
Stress Distributions ◽  
Uniform Shear ◽  
Sharp Stress ◽  
Close Form ◽  
Electric Loads

A two-dimensional electro-elastic analysis is performed on a transversely isotropic piezoelectric material with an elliptical hole, which is subjected to remote uniform shear forces, and remote electric field. Based on the impermeable electric boundary conditions, close form solutions are obtained by using the complex potentials method. Taking PZT-4 ceramic into consideration, the stress distributions around the neighborhood of the elliptical hole are given. It is shown that the hole geometry and the electric field are responsible for the shielding effect, there are sharp stress concentration near the hole.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

scholarly journals Exact statistical solution for the hopping transport of trapped charge via finite Markov jump processes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrey A. Pil’nik ◽  
Andrey A. Chernov ◽  
Damir R. Islamov
Keyword(s):  
Charge Transport ◽  
Thin Layers ◽  
Jump Processes ◽  
Dielectric Films ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Statistical Solution ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Thin Dielectric Films

AbstractIn this study, we developed a discrete theory of the charge transport in thin dielectric films by trapped electrons or holes, that is applicable both for the case of countable and a large number of traps. It was shown that Shockley–Read–Hall-like transport equations, which describe the 1D transport through dielectric layers, might incorrectly describe the charge flow through ultra-thin layers with a countable number of traps, taking into account the injection from and extraction to electrodes (contacts). A comparison with other theoretical models shows a good agreement. The developed model can be applied to one-, two- and three-dimensional systems. The model, formulated in a system of linear algebraic equations, can be implemented in the computational code using different optimized libraries. We demonstrated that analytical solutions can be found for stationary cases for any trap distribution and for the dynamics of system evolution for special cases. These solutions can be used to test the code and for studying the charge transport properties of thin dielectric films.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

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