On the theory of the elastic wave propagation in a crystal coated with a solid layer. II. Surface and leaky waves near a line of exceptional bulk waves

Darinskii, A.N.

doi:10.1098/rspa.2000.0594

Cited by 5 publications

(4 citation statements)

References 16 publications

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“…The analysis reveals that the orientations supporting LSAWs lie within particular 3D portions (sectors) of the orientation space. As in the case of layered substrates (Darinskii 2000), there are three possible shapes of these sectors (see Darinskii 2000, fig. 2). It may be that leaky solutions do not appear at all.…”

Section: (B) Transonic Statevmentioning

confidence: 99%

“…As for non-piezoelectric media Darinskii 2000), the eigenvectors ξ 3 and ξ 7 in the vicinity ofv are sought in the form…”

Section: Perturbation Theorymentioning

confidence: 99%

“…With this in mind, we confine ourselves to giving a number of expressions and some comments. More thorough discussion and corresponding figures can be found in Darinskii (2000).…”

Section: Surface and Leaky Quasi-bulk Wavesmentioning

confidence: 99%

“…Assuming that a limiting wave is exceptional at an orientation Ψ 0 of the substrate if the piezoeffect is ignored, we shall investigate possible surface and leaky solutions that arise for orientations close to Ψ 0 and speeds close to the trace speed of this exceptional wave when the piezoeffect is 'switched on'. Note that an analogous problem-the effect of a solid layer on EBWs in a non-piezoelectric substrate-has recently been studied by Darinskii (2000). It should also be said that the problem to be studied is directly related to the properties of high-velocity leaky and surface waves near the quasi-transverse and quasi-longitudinal branches that have been intensively studied numerically during recent years (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Quasi–bulk surface and leaky waves in piezoelectrics of unrestricted symmetry

Darinskii

Weihnacht

2003

Proc. R. Soc. Lond. A

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A theoretical study has been made of the effect of piezoelectric coupling on exceptional bulk waves (EBWs) that exist on the surface of a medium if the piezomoduli are made equal to zero. The analysis has been carried out assuming that the medium is of generic symmetry and that the piezoeffect is weak. In combination with elastic anisotropy, the piezoelectric coupling can cause the appearance of surface and leaky acoustic waves (SAWs and LSAWs) at orientations close to those supporting EBWs. The existence conditions for SAWs and LSAWs have been studied. In particular, it has been shown that the piezoeffect provides the existence of non-attenuating fast SAWs near the EBW associated with the branch of fast quasi-transverse bulk waves. Such an SAW appears independently of the crystallographic symmetry and material constants if the surface of the substrate is metallized. On the non-metallized surface, it may or may not exist, depending on the material constants. In addition, contrary to the case of non-piezoelectric media, quasi-longitudinal EBWs generally give rise to the leaky waves. Numerical computations for SiO 2 crystal confirm our analytic estimations.

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Section: (B) Transonic Statevmentioning

confidence: 99%

“…As for non-piezoelectric media Darinskii 2000), the eigenvectors ξ 3 and ξ 7 in the vicinity ofv are sought in the form…”

Section: Perturbation Theorymentioning

confidence: 99%

“…With this in mind, we confine ourselves to giving a number of expressions and some comments. More thorough discussion and corresponding figures can be found in Darinskii (2000).…”

Section: Surface and Leaky Quasi-bulk Wavesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quasi–bulk surface and leaky waves in piezoelectrics of unrestricted symmetry

Darinskii

Weihnacht

2003

Proc. R. Soc. Lond. A

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Linear and Nonlinear Wave Propagation in Coated or Uncoated Elastic Half-spaces

Waves in Nonlinear Pre-Stressed Materials

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In these lectures, we discuss the following three closely related topics.(i) Unification of different methods for deriving evolution equations for surface acoustic waves. Early studies on nonlinear surface acoustic waves were thwarted by very complicated derivation of evolution equations. Worse still, different methods seemed to have given different evolution equations. Later on, it became known that all these methods except one yield the same evolution equation, but even at the time when we started to prepare the current lecture notes, there still existed a method that does not agree with the other methods. Such a situation is unsatisfatory since each method has some following. The purpose of the lectures on this topic is three-fold. Firstly, we aim to show that derviation of the evolution eqution for nonlinear surface waves can be carried out in one A4 page even in the most general case. Secondly, we show that the odd method that used to give a different evolution equation can in fact be used to obtain the same evolution equation if it is properly executed. Thus, we set the record straight: all known methods should and do give the same evolution equation! Thirdly, we express our evolution equation in terms of results from the linear surface-wave theory built on the Stroh formulation, and we explain how the coefficients in the evolution equation can be evaluated efficiently.(ii) Linear wave propagation in a coated elastic half-space. This is partly in preparation for our discussion of the third topic, but the problem is of much interest in its own right. We show how the dispersion relation can be expressed elegantly in terms of the surface-impedance matrices associated with the layer and the half-space. We derive a two-term expression for the wave speed in the long-wavelength limit.(iii) Periodic and solitary waves in a coated elastic half-space. An uncoated elastic half-space cannot in general support solitary waves due to lack of dispersion although it has been argued previously that the nonlocal character of nonlinearity may give rise to the existence of steady travelling waves. We derive the nonlinear evolution equation for small-amplitude long-wavelength travellingThe original publication is available at www.springerlink.com http://www.springerlink.com/content/978-3-211-73571-8/#section=264495&page=2&locus=50 2 waves propagating in a coated elastic half-space where the thin coating induces weak dispersion. When this evolution equation is linearized, we recover the two-term dispersion relation obtained in (ii). We explain a simple method that can be used to compute periodic or solitary travelling-wave solutions.

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Characteristic features of the velocity dispersion of surface acoustic waves in anisotropic coated solids

Shuvalov

Every

2002

Ultrasonics

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On the theory of the elastic wave propagation in a crystal coated with a solid layer. II. Surface and leaky waves near a line of exceptional bulk waves

Cited by 5 publications

References 16 publications

Quasi–bulk surface and leaky waves in piezoelectrics of unrestricted symmetry

Quasi–bulk surface and leaky waves in piezoelectrics of unrestricted symmetry

Linear and Nonlinear Wave Propagation in Coated or Uncoated Elastic Half-spaces

Characteristic features of the velocity dispersion of surface acoustic waves in anisotropic coated solids

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