Nowacki Static and Dynamic Coupled Fields in Bodies with Piezoeffects or Polarization Gradient

1. Auflage 2010
ISBN: 978-3-540-31670-1
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 26, 209 Seiten

Reihe: Lecture Notes in Applied and Computational Mechanics

This book is devoted to the theory of coupled electro-magneto-thermo-elastic fields excited in different bodies by various sources, both static and dynamic. It presents the classical piezoelectric and piezomagnetic effects, the Mindlin's electroelastic coupling due to a polarization gradient, and different combinations of these effects with thermoelasticity.

Autoren/Hrsg.

Nowacki, Jerzy

Inhaltsverzeichnis

1;Table of Contents
;7
2;Introduction;10
3;Part I Two Types of Electro-Elastic Coupling and Their Role in Properties of Line Defects in Unbounded Anisotropic Media
;16
3.1;1 Piezoelectricity and Piezomagnetism: Basic Concepts and Equations
;17
3.1.1;1.1 Thermodynamic potentials
;17
3.1.2;1.2 Linear piezoelectricity;20
3.1.3;1.3 Piezomagnetic effects of linear and linearized origins;28
3.2;2 Mindlin's Electro-Elastic Coupling due to Polarization Gradient
;31
3.2.1;2.1 Toupin's alternative formulation of the theory of piezoelectricity
;31
3.2.2;2.2 Mindlin's extension of the classical theory of piezoelectricity
;34
3.2.3;2.3 Mindlin's equations for centrosymmetric and isotropic media
;40
3.2.4;2.4 Thermoelasticity of dielectrics with polarization gradient
;45
3.3;3 General Electro-Elastic Line Defec tin Unbounded Piezoelectric Body
;51
3.3.1;3.1 Dislocation and its electrostatic analog as a combined line defect
;51
3.3.2;3.2 Fundamental properties of 4D dislocations of arbitrary shape
;56
3.3.3;3.3 Electro-elastic fields of straight 4D dislocations;64
3.4;4 Thermo-Electro-Elastic Fields Accompanying Plastic Deformation
;76
3.4.1;4.1 Thermodynamics of plastic deformation in thermoelastic piezoelectrics
;76
3.4.2;4.2 Coupled fields produced by a moving straight dislocation
;80
3.4.3;4.3 The temperature distribution around a moving edge dislocation
;84
3.5;5 Some Extensions for Dislocation in Materials with Polarization Gradient
;93
3.5.1;5.1 Linear and surface definitions of a dislocation;93
3.5.2;5.2 The field of a straight dislocation;98
4;Part II 1D and 2D Electro-Elastic Coupled Fields in Media with Surfaces and Interfaces
;105
4.1;6 Coupled Fields of Thermal Inclusion in Media with Polarization Gradient
;106
4.1.1;6.1 Plain thermal inclusion in unbounded dielectric medium
;106
4.1.2;6.2 Thermal inclusion at the surface of a half-infinite dielectric
;112
4.1.3;6.3 Plain thermal inclusion in the middle of a dielectric plate
;115
4.1.4;6.4 Plain thermal inclusion at the surface of a dielectric plate
;120
4.1.5;6.5 Cylindrical thermal inclusion in an infinite dielectric medium
;125
4.1.6;6.6 Conclusions
;127
4.2;7 Green's Functions for Piezoelectric Strip with a General Line Source
;129
4.2.1;7.1 Statement of the problem and basic equations;129
4.2.2;7.2 Boundary conditions and their block representations;134
4.2.3;7.3 Green's function for the plate with free surfaces;137
4.2.4;7.4 Green's functions for plates with other boundary conditions
;143
4.2.5;7.5 Conclusions;145
4.3;8 Green's Functions for Piezoelectric Strip with Line Surface Sources
;146
4.3.1;8.1 Basic equations and boundary conditions;146
4.3.2;8.2 Strips with prescribed loads at both surfaces;150
4.3.3;8.3 Strips with prescribed displacements at both surfaces;158
4.3.4;8.4 Strips with prescribed displacements at one surface and loads at another
;163
4.3.5;8.5 Conclusions;169
4.4;9 2D Electro-Elastic Fields in a Piezoelectric Layer-Substrate Structure
;170
4.4.1;9.1 Basic equations;170
4.4.2;9.2 Boundary conditions at the surface and at the interface
;173
4.4.3;9.3 General and partial solutions for n(k,y) and n(x,y)
;175
4.4.4;9.4 Electro-elastic fields excited by the line source in the interior of the structure
;178
4.4.5;9.5 Electro-elastic fields excited at the surface of the structure
;184
4.4.6;9.6 Conclusions
;187
4.5;10 Acoustic Waves in Piezomagnetic and Piezoelectric Structures
;189
4.5.1;10.1 Bluestien-Gulyaev type surface waves in piezomagnetics
;189
4.5.2;10.2 Magnetoelastic SH waves in a bicrystalline gap structure
;192
4.5.3;10.3 Resonance excitation of Bluestein-Gulyaev waves
;196
4.5.4;10.4 Waveguide Sh acoustic modes in a piezoelictric plate
;200
5;References;205

Leseproben

"7 GREENS FUNCTIONS FOR PIEZOELECTRIC STRIP WITH A GENERAL LINE SOURCE (p. 125-126)

In this chapter we are going to derive the static Green function describing the 2D coupled fields in arbitrary piezoelectric strip excited by a general line defect parallel to the surfaces and consisting of the four line sources introduced in Sec. 3.3 (c): the line of forces f, the line of charge q, the straight dislocation with the Burgers vector b, and its electrostatic analog of the strength A(p. As we have seen in Ch. 3, the latter line defect is completely determined by the discontinuity Aip in the electrical potential across the arbitrary plane cut ending on the line, which in our case determines the coinciding positions of all the mentioned sources.

The first studies in this field were accomplished for a particular case of straight dislocations in isotropic elastic plates [55-59]. These results were later extended for anisotropic [53] and possibly inhomogeneous [54] purely elastic (nonpiezoelectric) infinite strips. The further extension of the theory for the case of arbitrary piezoelectric strips has been developed in our paper [28]. The content of Chapter 7 is based on this paper.

7.1 Statement of the problem and basic equations

(a) Some preliminary remarks

The aim of this chapter is a derivation of the electro-elastic fields excited in a piezoelectric plate by the general line defect defined above. Of course, such an object, as the general line defect first introduced by Lothe & Barnett [63], is only conventionally a "defect", because among its four constituent line sources there is only one lattice defect - the dislocation. So, perhaps, it would be more correct to talk about the general line source rather than about a defect.

Anyway, independently of the terminology introduced and accepted before us, below we are going to find the physical fields excited by such a combined source. In our analysis it will be convenient to follow the method developed in [54] for purely elastic anisotropic continuously layered media, specifying the problem to a homogeneous medium and simultaneously extending it for a piezoelectric case. Such an extension turns out to be not quite straightforward because of the electrical boundary conditions, which are determined by a continuity of the normal component of electric displacement on the interfaces between the strip and the adjoined isotropic dielectric media. Our consideration will be based on the Stroh-like approach presented in details in Chapter 3 (Sec. 3.3 (c)) where the problem was already formulated for the same general line defect in unbounded medium."