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.

Universal Relations in Piezoelectric Composites With Eigenstress and Polarization Fields, Part I: Binary Media—Local Fields and Effective Behavior

1993 ◽  
Vol 60 (2) ◽  
pp. 265-269 ◽  
Author(s):  
Y. Benveniste
Keyword(s):  
Spontaneous Polarization ◽  
Electric Field Intensity ◽  
Local Fields ◽  
Composite Media ◽  
Piezoelectric Composites ◽  
Arbitrary Phase ◽  
Electromechanical Loading ◽  
Piezoelectric Behavior ◽  
Binary Composite ◽  
Effective Constants

Binary composite media of arbitrary phase geometry are considered. The constituent phases have general anisotropic piezoelectric behavior and contain constant eigenstress and spontaneous polarization fields. An electromechanical loading of the composite aggregate is found which results in uniform strain and electric field intensity throughout the solid. The existence of these uniform fields is used to derive exact universal relations between the local fields as well as between the effective constants of the composite aggregate.

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.

scholarly journals Field statistics in nonlinear composites. II. Applications

2006 ◽  
Vol 463 (2077) ◽  
pp. 203-222 ◽  
Author(s):  
Martín I Idiart ◽  
Pedro Ponte Castañeda
Keyword(s):  
Transversely Isotropic ◽  
Second Order ◽  
Local Fields ◽  
Two Phase ◽  
Second Moments ◽  
Constituent Phase ◽  
Homogenization Methods ◽  
Exact Relations ◽  
Nonlinear Homogenization ◽  
Nonlinear Composites

Part I of this work provided a methodology for extracting the statistics of the local fields in nonlinear composites, from the effective potential of suitably perturbed composites. In particular, exact relations were given for the first and even moments of the fields in each constituent phase. In this part, use is made of these exact relations in the context of the ‘variational’, ‘tangent second-order’ and ‘second-order’ nonlinear homogenization methods to generate estimates for the phase averages and second moments of the fields for two-phase, power-law composites with isotropic and transversely isotropic microstructures. The accuracy of these estimates is assessed by confronting them against corresponding exact results for sequentially laminated composites. Among the nonlinear homogenization estimates considered in this work, the second-order estimates are found to be, in general, the most accurate, especially for large heterogeneity contrast and nonlinearity. Thus, these estimates are able to capture, for example, the strong anisotropy in the strain fluctuations that can develop inside nonlinear porous and rigidly reinforced composites.

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 Concerning the Local Fields and Effective Properties in Piezoelectric Composites

1994 ◽  
Vol 116 (3) ◽  
pp. 260-267 ◽  
Author(s):  
Y. Benveniste
Keyword(s):  
Effective Properties ◽  
Transversely Isotropic ◽  
Local Fields ◽  
The Other ◽  
Effective Moduli ◽  
Piezoelectric Composites ◽  
Arbitrary Phase ◽  
New Findings ◽  
Piezoelectric Solids ◽  
Underlying Theme

This paper consists of two parts: (a) a concise summary and discussion is given of the recent contributions of the author in the micromechanics of piezoelectric composites. The underlying theme here is the derivation of exact connections for the local fields and effective moduli of heterogeneous piezoelectric solids. Composites of arbitrary phase geometry as well as fibrous systems are considered. (b) New results are presented on the effective behavior of fibrous piezoelectric systems. Fibrous composites with transversely isotropic constituents and cylindrical microgeometry are considered. The exact connections of the author (Benveniste (1993), Proc. R. Soc., Series A, Vol. 441, pp. 59-81) are extended to include the most generally possible overall symmetry of the composite aggregate. The other category of the new findings concerns exact expressions for the effective thermal terms of fibrous systems which possess the same shear modulus GT.

scholarly journals Design and Fabrication of a Stacked Three-Phase Piezoelectric Composites Ring Array Underwater Ultrasound Transducer

Materials ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 5971
Author(s):  
Lili Xia ◽  
Hongwei Wang ◽  
Qiguo Huang
Keyword(s):  
Simulation Software ◽  
Piezoelectric Composite ◽  
Ultrasound Transducer ◽  
Voltage Response ◽  
Open Angle ◽  
Sound Waves ◽  
Forming Process ◽  
Piezoelectric Composites ◽  
Composite Ring ◽  
Three Phase

A stacked three-phase piezoelectric composites ring array underwater ultrasound transducer was developed in this paper. The circular structure of three-phase piezoelectric composite with a large open angle was improved based on the 1-3 piezoelectric composites. The structure size of the transducer’s sensitive component was designed by using ANSYS simulation software, and the single-ring samples of three-phase piezoelectric composites with different thicknesses were fabricated. Based on the bandwidth broadening theory of multimode coupled vibration, the piezoelectric composite ring-shaped sensitive component was fabricated by the piezoelectric composite curved-surface-forming process. According to the design structure of the transducer, the stacked three-phase piezoelectric composites ring array underwater ultrasound transducer was processed. The experimental results show that the maximum transmission voltage response is 154 dB, the open angle of the horizontal beam reaches 360°, and the bandwidth of −3 dB is 86 kHz. The developed transducers achieved a high frequency, broadband, and large open angle to radiate sound waves.

scholarly journals Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1259
Author(s):  
Francisco G. Montoya ◽  
Raúl Baños ◽  
Alfredo Alcayde ◽  
Francisco Manuel Arrabal-Campos ◽  
Javier Roldán Roldán Pérez
Keyword(s):  
Geometric Algebra ◽  
Dimensional Euclidean Space ◽  
Active Components ◽  
Electrical Circuits ◽  
Current Harmonics ◽  
Operation Conditions ◽  
Multiple Phase ◽  
Three Phase ◽  
Phase Systems ◽  
Definition Of

This paper presents a new framework based on geometric algebra (GA) to solve and analyse three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an exploratory application of the geometric algebra power theory (GAPoT) to multiple-phase systems. A definition of geometric apparent power for three-phase systems, that complies with the energy conservation principle, is also introduced. Power calculations are performed in a multi-dimensional Euclidean space where cross effects between voltage and current harmonics are taken into consideration. By using the proposed framework, the current can be easily geometrically decomposed into active- and non-active components for current compensation purposes. The paper includes detailed examples in which electrical circuits are solved and the results are analysed. This work is a first step towards a more advanced polyphase proposal that can be applied to systems under real operation conditions, where unbalance and asymmetry is considered.

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