Wave propagation in transversely isotropic elastic media - II. Surface waves

1989 ◽  
Vol 422 (1862) ◽  
pp. 67-101 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Theoretical Background ◽  
Clear Understanding ◽  
Elastic Media ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

The treatment of homogeneous plane waves given in part I provides the basis for the detailed study of the nature of surface-wave propagation in transversely isotropic elastic media presented in this paper. The investigation is made within the framework of the existence theorem of Barnett and Lothe and the developments underlying its proof. The paper begins with a survey of this essential theoretical background, outlining in particular the formulation of the secular equation for surface waves in the real form F(v) = 0, F(v) being a nonlinear combination of definite integrals involving the acoustical tensor Q (⋅) and the associated tensor R (⋅,⋅) introduced in part I. The calculation of F(v) for a transversely isotropic elastic material is next undertaken, first, in principle, for an arbitrary orientation of the axis of symmetry, then for the α and β configurations, shown in part I to contain all the exceptional transonic states. In the rest of the paper the determination of F(v) is completed, in closed form, for the α and β configurations and followed in each case by a discussion of the properties of F(v) and illustrative numerical results. This combination of analysis and computation affords a clear understanding of surface-wave behaviour in the exceptional configurations comprising, in the classification of part I, cases 1, 2 and 3. The findings for case 1 exhibit continuous transitions, within the α configurations, between subsonic and supersonic surface-wave propagation. Those for case 3 prove that there are discrete orientations of the axis for which no genuine surface wave can propagate and that this degeneracy typically has a marked influence on surface-wave properties in a sizeable sector of neighbouring β configurations. Neither effect appears in previous accounts of surface-wave propagation in anisotropic elastic media.

On the existence of type-6 transonic states in linear elastic media of cubic symmetry

1987 ◽  
Vol 411 (1840) ◽  
pp. 251-263 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Solid ◽  
Mechanics Of Solids ◽  
Elastic Media ◽  
Slowness Surface ◽  
Cubic Symmetry ◽  
Linear Elastic ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

Crucial to the understanding of surface-wave propagation in an anisotropic elastic solid is the notion of transonic states, which are defined by sets of parallel tangents to a centred section of the slowness surface. This study points out the previously unrecognized fact that first transonic states of type 6 (tangency at three distinct points on the outer slowness branch S 1 ) indeed exist and are the rule, rather than the exception, in so-called C 3 cubic media (satisfying the inequalities c 12 + c 44 > c 11 - c 44 > 0); simple numerical analysis is used to predict orientations of slowness sections in which type-6 states occur for 21 of the 25 C 3 cubic media studied previously by Chadwick & Smith (In Mechanics of solids , pp. 47-100 (1982)). Limiting waves and the composite exceptional limiting wave associated with such type-6 states are discussed.

Experimental observation of surface wave propagation for a transversely isotropic medium

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 185-190 ◽  
Author(s):  
Chih‐Hsiung Chang ◽  
Gerald H. F. Gardner ◽  
John A. McDonald
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Transversely Isotropic ◽  
Insulation Material ◽  
Velocity Anisotropy ◽  
Vertical Seismic Profiling ◽  
Surface Wave Propagation ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Velocity anisotropy of surface‐wave propagation in a transversely isotropic solid has been observed in a laboratory study. In this study, Phenolite™, an electrical insulation material, was used as the transversely isotropic media (TIM), and a vertical seismic profiling (VSP) geometry was used to record seismic arrivals and to separate surface waves from shear waves. Results show that surface waves that propagate with different velocities exist at certain directions.

Surface waves on water of non-uniform depth

1958 ◽  
Vol 4 (6) ◽  
pp. 607-614 ◽  
Author(s):  
Joseph B. Keller
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Linear Theory ◽  
Gravity Waves ◽  
Geometrical Optics ◽  
Surface Wave Propagation ◽  
Special Cases

Gravity waves occur on the surface of a liquid such as water, and the manner in which they propagate depends upon its depth. Although this dependence is described in principle by the equations of the ‘exact linear theory’ of surface waves, these equations have not been solved except in some special cases. Therefore, oceanographers have been unable to use the theory to describe surface wave propagation in water whose depth varies in a general way. Instead they have employed a simplified geometrical optics theory for this purpose (see, for example, Sverdrup & Munk (1944)). It has been used very successfully, and consequently various attempts, only partially successful, have been made to deduce it from the exact linear theory. It is the purpose of this article to present a derivation which appears to be satisfactory and which also yields corrections to the geometrical optics theory.

Surface Wave Propagation in Thin Silver and Aluminium Films

2005 ◽  
Vol 60 (11-12) ◽  
pp. 789-796
Author(s):  
Anouar Njeh ◽  
Nabil Abdelmoula ◽  
Hartmut Fuess ◽  
Mohamed Hédi Ben Ghozlen
Keyword(s):  
Thin Films ◽  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Acoustic Waves ◽  
Frequency Interval ◽  
Constant Frequency ◽  
Surface Wave Propagation ◽  
Coated Materials ◽  
Bulk Waves

Three kinds of acoustic waves are known: bulk waves, pseudo-surface waves and surface waves. A plane wave section of a constant-frequency surface of a film serves as a hint for the expected nature. Calculations based on slowness curves of films reveal frequency ranges where each type of acoustic waves is predominant. Dispersion curves and displacement acoustic waves are calculated and commented in each frequency interval for different coated materials. Both dispersion and sagittal elliptical displacement are sensitive and depend on diagrams mentioned above. Silver and aluminium thin films having different anisotropy ratios, namely 2.91 and 1.21, are retained for illustration.

scholarly journals ON SURFACE WAVES IN A FINITELY DEFORMED MAGNETOELASTIC HALF-SPACE

2011 ◽  
Vol 03 (04) ◽  
pp. 633-665 ◽  
Author(s):  
P. SAXENA ◽  
R. W. OGDEN
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Wave Speed ◽  
Sagittal Plane ◽  
Isotropic Energy ◽  
Surface Wave Propagation ◽  
Homogeneous Strain

Rayleigh-type surface waves propagating in an incompressible isotropic half-space of nonconducting magnetoelastic material are studied for a half-space subjected to a finite pure homogeneous strain and a uniform magnetic field. First, the equations and boundary conditions governing linearized incremental motions superimposed on an initial motion and underlying electromagnetic field are derived and then specialized to the quasimagnetostatic approximation. The magnetoelastic material properties are characterized in terms of a "total" isotropic energy density function that depends on both the deformation and a Lagrangian measure of the magnetic induction. The problem of surface wave propagation is then analyzed for different directions of the initial magnetic field and for a simple constitutive model of a magnetoelastic material in order to evaluate the combined effect of the finite deformation and magnetic field on the surface wave speed. It is found that a magnetic field in the considered (sagittal) plane in general destabilizes the material compared with the situation in the absence of a magnetic field, and a magnetic field applied in the direction of wave propagation is more destabilizing than that applied perpendicular to it.

The behaviour of elastic surface waves polarized in a plane of material symmetry. I. Addendum

1991 ◽  
Vol 433 (1889) ◽  
pp. 699-710 ◽  
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Point Of View ◽  
Reference Plane ◽  
Material Symmetry ◽  
Reflected Waves ◽  
Inhomogeneous Plane ◽  
Symmetric Surface

This addition to a recent paper by Chadwick ( Proc. R. Soc. Lond . A 430, 213 (1990); hereafter referred to as part I) has been prompted mainly by the discovery of secluded supersonic surface waves propagating in configurations of transversely isotropic elastic media in which the reference plane is not a plane of material symmetry and coexisting with a subsonic surface wave. The occurrence of a supersonic surface wave travelling in a direction e 1 with speed v s implies that there are two homogeneous plane waves, with slowness vectors s i and s r such that s i . e 1 = S r . e 1 = v -1 s , which comprise the incident and reflected waves in a case of simple reflection at the traction-free boundary. Supersonic surface waves may therefore be found by searching within a suitably defined space of simple reflection, R . This is the approach which has led to the new results mentioned above and the principal conclusions of part I are re-examined here from the same point of view. It is found that, whereas the secluded supersonic surface waves in transversely isotropic media correspond to isolated points on a curvilinear projection of R which does not intersect the curve representing subsonic surface waves, the symmetric surface waves studied in part I define a curve which may lie partly inside and partly outside a projection of R in the form of a region, the interior points representing supersonic and the exterior points subsonic surface waves. This discussion is preceded by a simplification of the existence-uniqueness theorem proved in part I and followed by a reconsideration of the possibility that an inhomogeneous plane elastic wave can qualify as a surface wave. Such one-component surface waves do exist, but a symmetric surface wave necessarily contains two inhomogeneous plane waves.

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