Interfacial waves in incompressible monoclinic materials with an interlayer

Nair, Sudhakar; Sotiropoulos, D. A.

doi:10.1016/s0167-6636(98)00069-6

Cited by 21 publications

(17 citation statements)

References 7 publications

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“…The incompressible case was first studied by Nair and Sotiropoulos [3], although they did not establish the secular equation explicitly. The secular equation for incompressible materials can be deduced directly from (4.1) by imposing the incompressibility conditions s ′ 2β = −s ′ 1β .…”

Section: Secular Equation For Surface Waves In Incompressible Monoclimentioning

confidence: 99%

“…For compressible materials the secular equation was obtained explicitly for monoclinic materials with the symmetry plane at x 3 = 0 [1,2]. At the same time, some attention has been given to the consideration of interface waves in anisotropic materials which are incompressible (see for instance [3] or [4], and the references therein). In this paper we show that results obtained in the general (compressible) case can be easily specialized to the incompressible case, simply by imposing the conditions for incompressibility on the elastic compliances, without having to introduce an arbitrary pressure.…”

Section: Introductionmentioning

confidence: 99%

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The incompressible limit in linear anisotropic elasticity, with applications to surface waves and elastostatics

Destrade

Martin

Ting

2002

Journal of the Mechanics and Physics of Solids

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Incompressibility is established for three-dimensional and two-dimensional deformations of an anisotropic linearly elastic material, as conditions to be satisfied by the elastic compliances. These conditions make it straightforward to derive results for incompressible materials from those established for the compressible materials. As an illustration, the explicit secular equation is obtained for surface waves in incompressible monoclinic materials with the symmetry plane at x 3 = 0. This equation also covers the case of incompressible orthotropic materials.The displacements and stresses for surface waves are often expressed in terms of the elastic stiffnesses, which can be unbounded in the incompressible limit. An alternative formalism in terms of the elastic compliances presented recently by Ting is employed so that surface wave solutions in the incompressible limit can be obtained. A different formalism, also by Ting, is employed to study the solutions to two-dimensional elastostatic problems.In the special case of incompressible monoclinic material with the symmetry plane at x 3 = 0, one of the three Barnett-Lothe tensors S vanishes while the other two tensors H and L are the inverse of each other. Moreover, H and L are diagonal with the first two diagonal elements being identical. An interesting physical phenomenon deduced from this property is that there is no interpenetration of the interface crack surface in an incompressible bimaterial. When only the inplane deformation is considered, it is shown that the image force due to a line dislocation in a half-space or in a bimaterial depends only on the magnitude, not on the direction, of the Burgers vector.

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Section: Secular Equation For Surface Waves In Incompressible Monoclimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The incompressible limit in linear anisotropic elasticity, with applications to surface waves and elastostatics

Destrade

Martin

Ting

2002

Journal of the Mechanics and Physics of Solids

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“…Now a numerical example is given, as the surface wave speed is computed in the case (Nair and Sotiropoulos, 1999) where b ¼ 0:3 and d ¼ 0:1. Then, the secular equation (49) …”

Section: Incompressible Monoclinic Materialsmentioning

confidence: 99%

“…Then the results are specialized from monoclinic to orthorhombic symmetry. Finally, the constraint of incompressibility is taken into account, and a numerical problem left open by Nair and Sotiropoulos (1999) is resolved.…”

Section: Introductionmentioning

confidence: 99%

Rayleigh waves in symmetry planes of crystals: explicit secular equations and some explicit wave speeds

Destrade

2003

Mechanics of Materials

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Rayleigh waves are considered for crystals possessing at least one plane of symmetry. The secular equation is established explicitly for surface waves propagating in any direction of the plane of symmetry, using two different methods. This equation is a quartic for the squared wave speed in general, and a biquadratic for certain directions in certain crystals, where it may itself be solved explicitly. Examples of such materials and directions are found in the case of monoclinic crystals with the plane of symmetry at x 3 ¼ 0. The cases of orthorhombic materials and of incompressible materials are also treated.

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“…Zaitsev et al (2001) discussed propagation of acoustic waves in piezoelectric conductive and viscous plates. The supplement of surface wave analysis and other wave propagation problems to anisotropic elastic materials has been a subject of many studies; see for example Musgrave (1959), Crampin and Taylor (1971), Chadwick and Smith (1977), Dowaikh and Ogden (1990), Mozhaev (1995), Nair and Sotiropoulos (1999), Destrade (2001Destrade ( , 2003, Ting (2002), Singh (2011, 2014).…”

Section: Introductionmentioning

confidence: 99%

Modelling of SH-waves in a fiber-reinforced anisotropic layer over a pre-stressed heterogeneous half-space

Kakar

Kakar²

2015

jtam

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Modelling of SH-waves in an anisotropic fiber-reinforced layer provides a great deal of support in the understanding of seismic wave propagation. This paper deals with the propagation of SH-waves in a fiber-reinforced anisotropic layer over a pre-stressed heterogeneous half-space. The heterogeneity of the elastic half-space is caused by linear variations of density and rigidity. As a special case when both media are homogeneous and stress free, the derived equation is in agreement with the general equation of the Love wave. Numerically, it is observed that the velocity of SH-waves decreases with an increase in heterogeneity-reinforced parameters and decrease in initial stress.

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Interfacial waves in incompressible monoclinic materials with an interlayer

Cited by 21 publications

References 7 publications

The incompressible limit in linear anisotropic elasticity, with applications to surface waves and elastostatics

The incompressible limit in linear anisotropic elasticity, with applications to surface waves and elastostatics

Rayleigh waves in symmetry planes of crystals: explicit secular equations and some explicit wave speeds

Modelling of SH-waves in a fiber-reinforced anisotropic layer over a pre-stressed heterogeneous half-space

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