Pulse propagation in a transversely isotropic half-space

Ryan, R. L.

doi:10.1016/0022-460x(71)90578-5

Cited by 7 publications

(4 citation statements)

References 7 publications

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“…Indeed, Lamb's original problem is generally shown in textbooks on wave motion in elastic solids since it considers isotropic materialsthe expressions for displacements in the wavefield are compact and readily interpreted [1,3,23]. The extension to anisotropic materials and point sources requires effort but yields rich results that go well beyond those to be exploited here [24][25][26][27][28][29][30][31]. Fortunately, line source excitation of transversely anisotropic half-spaces has also been considered in some detail and the essential mathematical techniques required to derive solutions is generally no more involved than those used for isotropic materials [32][33][34].…”

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confidence: 99%

Line source representations for shear wave birefringence measurements in transversely isotropic materials using laser ultrasonics

Spicer

Zeng

2016

Wave Motion

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Line source representations for thermoelastic, laser excitation of transversely isotropic materials are developed to model shear wave birefringence effects that can occur in these materials. Continuum descriptions for elastic wave propagation are used to generate equations of motion that are solved using transform methods. Analytical solutions are presented for epicentral waveforms for propagation parallel and perpendicular to the axis of symmetry. These solutions are particularly simple and allow for rapid examination of the influence of various components of the stiffness tensor on wave propagation. In particular, for propagation perpendicular to the axis of symmetry, line source orientation parallel and perpendicular to this axis yield two cases that demonstrate shear wave birefringence. This effect is computed for titanium as well as for a nearly isotropic materialboth Class Ito highlight the influence of diagonal as well as offdiagonal components of the stiffness tensor on the character of laser ultrasonic waveforms when the tensor is referenced to the principal coordinate system. The results presented in this work should be used to guide the interpretation of laser ultrasonic, line source measurements in transversely isotropic materials when birefringence effects are present.

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confidence: 99%

Line source representations for shear wave birefringence measurements in transversely isotropic materials using laser ultrasonics

Spicer

Zeng

2016

Wave Motion

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“…Only numerical results were presented for the surface displacement at the (111) plane of cubic copper, and the RW and leaky SAW were identified. The case of a point source, applied at the surface of TI solids with its normal coinciding with the axis of symmetry, has been treated in a similar way by Ryan [96]. In contrast with the 2D problem, the 3D Lamb's problem does not admit an explicit solution for the surface displacements.…”

Section: Transient Propagationmentioning

confidence: 99%

Elastic surface waves in crystals. Part 1: Review of the physics

et al. 2011

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We present a review of wave propagation at the surface of anisotropic media (crystal symmetries). The physics for media of cubic and hexagonal symmetries has been extensively studied based on analytical and semi-analytical methods. However, some controversies regarding surfaces waves and the use of different notations for the same modes require a review of the research done and a clarification of the terminology. In a companion paper we obtain the full-wave solution for the wave propagation at the surface of media with arbitrary symmetry (including cubic and hexagonal symmetries) using two spectral numerical modeling algorithms.

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“…There is clearly a need to develop models for interpretation of data gathered in transversely isotropic materials systems [17][18][19]. The purpose of the work presented here is to provide descriptions of material displacements in the wavefield surrounding a subsurface, thermoelastic line source in a transversely isotropic half space.…”

Section: Introductionmentioning

confidence: 99%

Subsurface, thermoelastic line source excitation of a transversely isotropic half space

2017

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In this work, mathematical descriptions of material displacements in the wavefield surrounding a subsurface, thermoelastic line source in a transversely isotropic half space are given. These are derived from continuum representations that yield wave equations describing material motion that are solved using transform techniques. These solutions provide insight into the overall character of these sources in anisotropic materials and can also be used to model more generalized source distributions that might occur in a range of physical systems. Analytical, closed form solutions for epicentral displacements are derived and are graphically represented for particular source locations below the surface of a titanium half space. These results illustrate general aspects of the wavefield including the nature of various component modes of the displacement waveform. Wavefront characteristics associated with these modes are considered along with the nature of direct shear wave emission by this type of source. Mathematical results for displacements are used to illustrate how the surface-borne thermoelastic line source can be represented as a surface, shear stress dipole and are also used to represent more complicated subsurface source distributions that might occur in physical systems.

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Pulse propagation in a transversely isotropic half-space

Cited by 7 publications

References 7 publications

Line source representations for shear wave birefringence measurements in transversely isotropic materials using laser ultrasonics

Line source representations for shear wave birefringence measurements in transversely isotropic materials using laser ultrasonics

Elastic surface waves in crystals. Part 1: Review of the physics

Subsurface, thermoelastic line source excitation of a transversely isotropic half space

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