Reflection and refraction of plane quasi-longitudinal waves at an interface of two piezoelectric media under initial stresses
TL;DR: In this article, the problem of reflection and refraction of quasi-longitudinal waves under initial stresses at an interface of two anisotropic piezoelectric media with different properties was studied.
Abstract: This paper is devoted to study a problem of reflection and refraction of quasi-longitudinal waves under initial stresses at an interface of two anisotropic piezoelectric media with different properties. One of the two media is aluminum nitride, which is considered the down piezoelectric medium and the above medium is chosen as PZT-5H ceramics. The two piezoelectric media welded are assumed to be anisotropic of a type of a transversely isotropic crystals (hexagonal crystal structure, class 6 mm). The equations of motion and constitutive relations for the piezoelectric media have been written. Suitable boundary conditions are used to obtain the reflection and refraction coefficients. For an incidence of quasi-longitudinal plane waves, four independent-type amplitude ratios of elastic displacement components for plane waves, called quasi-longitudinal (qP) and quasi-shear vertical (qSV) waves, are shown to exist. Also, it is observed that there exist four dependent amplitude ratios of electric potential, which are proportional to the previous four types. Finally, it is found that the coefficients of reflection and refraction are functions of angle of incidence, elastic constants, piezoelectric potential parameters and the initial stresses. Numerical computations and the results obtained are depicted graphically. In the end, a particular case has been reduced from the present study. This investigation is considered important because the initial stresses in such practical problems are inevitable and may result in frequency shift, a change in the velocity of surface waves and controlling the selectivity of a filter compensation of the devices.
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TL;DR: In this article, the effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces are studied, and the algebraic equations resulting from the interface conditions are solved to obtain the amplitude ratio of various waves and furthermore the energy reflection coefficients of different waves.
58 citations
TL;DR: In this paper, a shape optimization technique based on the time-domain dual reciprocity boundary element method (DRBEM) was proposed to solve the two-temperature generalized magneto-thermoelastic problems.
Abstract: The main purpose of this article is to propose an efficient shape optimization technique based on the time-domain dual reciprocity boundary element method (DRBEM) to solve the two-temperature generalized magneto-thermoelastic problems. An implicit differentiation method was used to compute the shape design sensitivity of an approximate DRBEM solution with respect to design variables. The feasible direction method was suggested and implemented for use with the golden-section search technique for minimizing the weight objective function while satisfying all constraints. The optimum shape design of a square plate with a hole is used as the numerical example to verify the accuracy of the proposed technique.
43 citations
TL;DR: In this paper, the basic equations of motion, of Gauss and of heat conduction, together with constitutive relations for pyro- and piezoelectric media, are presented.
Abstract: In this paper, 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 qP, 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 semi-infinite, 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 (qP-wave) 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, electric, thermal constants. This study is relevant to signal processing, sound systems, wireless communications, surface acoustic wave devices and military defense equipment.
39 citations
TL;DR: In this paper, a solution based on the inhomogeneous wave theory is developed to address the inconsistency between the number of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients.
Abstract: This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.
35 citations
Cites background or methods from "Reflection and refraction of plane ..."
...Many efforts [2–8] have been devoted to the issue, and it has been found that one can consider only the elastic boundary conditions [4] if the piezoelectric effect is weak....
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...[5] used the reduced boundary conditions to obtain the reflection and refraction coefficients for a quasi-longitudinal incident wave, which was later adopted by Singh [6] in solving the reflection problem of a prestressed piezoelectric medium....
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TL;DR: In this article, the effects of mechanically and dielectrically imperfect interfaces on dispersion relations of elastic waves in a one-dimensional piezoelectric phononic crystal are studied.
32 citations
References
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Book•
01 Jan 1973
TL;DR: In this article, the authors apply the material developed in the Volume One to various boundary value problems (reflection and refraction at plane surfaces, composite media, waveguides and resonators).
Abstract: This work, part of a two-volume set, applies the material developed in the Volume One to various boundary value problems (reflection and refraction at plane surfaces, composite media, waveguides and resonators). The text also covers topics such as perturbation and variational methods.
5,211 citations
Book•
01 Jan 1962
TL;DR: In this article, the linearized theory of elasticity was introduced and the elasticity of a one-dimensional motion of an elastic continuum was modeled as an unbound elastic continuum.
Abstract: Preface Introduction 1 One-dimensional motion of an elastic continuum 2 The linearized theory of elasticity 3 Elastodynamic theory 4 Elastic waves in an unbound medium 5 Plane harmonic waves in elastic half-spaces 6 Harmonic waves in waveguides 7 Forced motions of a half-space 8 Transient waves in layers and rods 9 Diffraction of waves by a slit 10 Thermal and viscoelastic effects, and effects of anisotrophy and non-linearity Author Index Subject Index
4,133 citations
Additional excerpts
...References: Achenbach J.D., “Wave propagation in elastic solids”, North-Holland Publishing CompanyAmsterdam, Vol. 16, (1973). [1]...
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Book•
01 Jan 1988
176 citations
TL;DR: In this paper, a unified approach to the study of reflection and refraction of elastic waves in general anisotropic media is presented, where the Christoffel equations and boundary conditions for both anisometric media in coordinate systems formed by incident and interface planes, rather than in crystallographic coordinates, are considered.
Abstract: A unified approach to the study of reflection and refraction of elastic waves in general anisotropic media is presented. Christoffel equations and boundary conditions for both anisotropic media in coordinate systems formed by incident and interface planes, rather than in crystallographic coordinates, are considered. Consideration of wave propagation in an acoustic‐axis direction is included in the general algorithm, so results can be obtained both generally and for planes of symmetry, including planes of isotropy. General features of the numerical results are discussed. Energy conversion coefficients are shown to satisfy reciprocity relations which are formulated. It is much more natural to consider intensity–conversion ratios, rather than amplitude–conversion ratios, showing the important role of ray (rather than wave‐vector) directions in describing phenomena such as grazing angles. In particular, it is shown that the incident wave vector for grazing incidence may be greater or less than 90°: The domain of incident wave‐vector angles can actually split into disjoint pieces. The reflection coefficient at grazing incidence is shown to be unity, as in the isotropic case. Critical‐angle phenomena are described naturally by this approach.
168 citations
"Reflection and refraction of plane ..." refers background in this paper
...The propagation of body waves in anisotropic media is fundamentally different from their propagation in isotropic media, although the differences may be comparatively subtle and difficult to observe (see [3,4,8,14,15, 18 ])....
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