الفهرس 
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Abstract
propagation of plane waves in thermo-piezoelectric media with
thermal relaxation times in the framework of generalized theories of
thermoelasticity has been become a topic for a lot of investigations in
recent years.
These investigations are considered to be important because of their
possible extensive applications in various branches of science and
technology. They also have a lot of applications in many natural scientific
fields such as: astrophysics, geophysics, seismology, acoustics, radio
electronics, communications and computer technology.
The principal aim of this thesis is to investigate and find solutions of
some problems associated with wave propagation in thermo-piezoelectric
media under the effect of thermal relaxation times.
This thesis consists of five chapters, some appendixes, Arabic abstract,
English summary and a list of references. The contents of the chapters
may be reviewed as follows:
Chapter one:
In this chapter, we present a general introduction on the subject of this
thesis, and we recall some of the useful definitions and many of basic
concepts. Next, the importance of the piezoelectric, thermoelastic and
thermo-piezoelectric materials is introduced. Finally, the basic equations
and constitutive relations for an anisotropic thermo-piezoelectric
materials with the existence the thermal relaxation times are given.
Chapter two:
The objective of this chapter is to study the bulk acoustic wave (BAW)
propagation velocities in transversely isotropic piezoelectric materials,
Aluminum Nitride, Zinc Oxide, Cadmium sulfide and Cadmium Selenide.
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The BAW velocities are computed for each direction by solving the
Christoffel’s equation based on the theory of acoustic waves in anisotropic
solids exhibiting piezoelectricity. These values are calculated numerically
and implemented on a computer by Bisection Method Iterations
Technique (BMIT). The modifications of the BAW velocities caused by
the piezoelectric effect are graphically compared with the velocities in the
corresponding non-piezoelectric materials. The results obtained in this
study can be applied to signal processing, sound systems and wireless
communication in addition to the improvement of surface acoustic wave
(SAW) devices and military defense equipment.
Chapter three:
In this chapter, the well-established two-dimensional mathematical model
for linear pyroelectric materials is employed to investigate the reflection
of waves at the boundary between a vacuum and an elastic, transversely
isotropic, pyroelectric material. A comparative study between the
solutions of (a) classical thermoelasticity, (b) Lord-Shulman theory and
(c) Green-Lindsay theory equations, characterized by none, one and two
relaxation times respectively, is presented. Suitable boundary conditions
are considered in order to determine the reflection coefficients when
incident elasto-electro-thermal waves impinge the free interface. It is
established that, in the quasi-electrostatic approximation, three different
classes of waves: (i) two principally elastic waves, namely, a quasilongitudinal
Primary (qP) wave and a quasi-transverse Secondary (qS)
wave; and (ii) a mainly thermal (qT) wave. The observed electrical effects
are, on the other hand, a direct consequence of mechanical and thermal
phenomena due to pyroelectric coupling. The computed reflection
coefficients of plane qP waves are found to depend upon the angle of
incidence, the elastic, electric and thermal parameters of the medium, as
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well as the thermal relaxation times. Finally, the reflection coefficients
are computed for Cadmium selenide (CdSe) observing the influence of (i)
the anisotropy of the material, (ii) the electrical potential and (iii)
temperature variations and (iv) the thermal relaxation times on the
reflection coefficients.
Chapter four:
In this chapter, the basic equations of motion, of Gauss and of heat
conduction, together with constitutive relations for pyro- and piezoelectric
media, are presented. Three thermoelastic theories are considered:
classical dynamical coupled theory, the Lord–Shulman theory with one
relaxation time and Green and Lindsay theory with two relaxation times.
For incident elastic longitudinal, potential electric and thermal waves,
referred to as q P, φ-mode and T-mode waves, which impinge upon the
interface between two different transversal isotropic media, reflection and
refraction coefficients are obtained by solving a set of linear algebraic
equations. A case study is investigated: a system formed by two semiinfinite,
hexagonal symmetric, pyroelectric–piezoelectric media, namely
Cadmium Selenide (CdSe) and Barium Titanate (BaTiO3). Numerical
results for the reflection and refraction coefficients are obtained, and their
behavior versus the incidence angle is analyzed. The interaction with the
interface give rises to different kinds of reflected and refracted waves: (i)
two reflected elastic waves in the first medium, one longitudinal (qPwave)
and the other transversal (qSV-wave), and a similar situation for the
refracted waves in the second medium; (ii) two reflected potential electric
waves and a similar situation for the refracted waves; (iii) two reflected
thermal waves and a similar situation for the refracted waves. The
amplitudes of the reflected and refracted waves are functions of the
incident angle, of the thermal relaxation times and of the media elastic,
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electric, thermal constants. This study is relevant to signal processing,
sound systems, wireless communications, surface acoustic wave devices
and military defense equipment.
Chapter Five:
In this chapter, a mathematical model of the effect of the rotation on
horizontally shear wave (SH-wave) propagation in a piezoelectric halfspace
covered by a semiconductor film is investigated analytically. The
semiconducting layer is rotating with a uniform angular velocity. The
interface between the piezoelectric substrate and the semiconductor layer
is imperfectly bonded. The surfaces of the bilayer system are free of
traction, electrically shorted or open are considered. The governing
equations of the mechanical displacement and electrical potential function
under the effect of rotation are obtained by solving the coupled
electromechanical field equations of the piezoelectric half-space and the
semiconductor film. The exact frequency equations of SH waves are
derived.
The numerical examples are given to illustrate the effects of rotation and
electromagnetic boundary conditions, the different values of the film
thickness and wave number on the dispersion behaviors. Finally, the
effect of the rotation on the frequency equation is investigated in detail
for piezoelectric ceramics PZT-5H and semiconductor silicon. The
obtained results provide a predictable and theoretical basis for
applications of piezoelectric and semiconductor composites to acoustic
wave devices.