Some New Ideas in the Theory of Surface Acoustic Waves in Anisotropic Media

Mozhaev, V.G.

doi:10.1007/978-94-015-8494-4_63

Cited by 28 publications

(43 citation statements)

References 9 publications

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“…The material is monoclinic with the symmetry plane at x 3 = 0. In the general (compressible) case the secular equation for the surface wave has been obtained explicitly by Destrade [1] using the method of first integrals introduced by Mozhaev [21], and by Ting [2] using a modified Stroh [22] formalism. Letting X = ρv 2 where ρ is the mass density, the secular equation is…”

Section: Secular Equation For Surface Waves In Incompressible Monoclimentioning

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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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%

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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“…where Γ = 1, 2, k is the real wave number, v is the real wave speed of propagation, and the specific dependence of the amplitudes U Γ and P on x 2 need not be specified [23]. Consequently, the incremental Bell constraint (2.11) now reduces to…”

Section: Principal Surface Wavesmentioning

confidence: 99%

“…Interestingly, although Rayleigh treated the case of incompressibility in his paper, surface waves propagating in internally constrained, triaxially prestressed, elastic materials received only tardy attention (see for instance Dowhaik and Ogden [20], Chadwick [21], or Rogerson [22].) Recently this paper's author proposed a method, inspired by Mozhaev [23], to derive the explicit secular equation for surface acoustic waves in monoclinic elastic crystals [24]. In that paper, it was claimed that taking the first integrals of the tractions rather than of the displacements (as in [23]) to obtain the secular equation was a procedure that could 'easily accommodate internal constraints.'…”

Section: Introductionmentioning

confidence: 99%

“…Recently this paper's author proposed a method, inspired by Mozhaev [23], to derive the explicit secular equation for surface acoustic waves in monoclinic elastic crystals [24]. In that paper, it was claimed that taking the first integrals of the tractions rather than of the displacements (as in [23]) to obtain the secular equation was a procedure that could 'easily accommodate internal constraints.' Here this claim is validated by the consideration of the Bell constraint for small amplitude surface waves travelling in a principal direction of a homogeneously deformed half-space.…”

Section: Introductionmentioning

confidence: 99%

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Surface waves in deformed Bell materials

Destrade

2003

International Journal of Non-Linear Mechanics

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Small amplitude inhomogeneous plane waves are studied as they propagate on the free surface of a predeformed semi-infinite body made of Bell constrained material. The predeformation corresponds to a finite static pure homogeneous strain. The surface wave propagates in a principal direction of strain and is attenuated in another principal direction, orthogonal to the free surface. For these waves, the secular equation giving the speed of propagation is established by the method of first integrals. This equation is not the same as the secular equation for incompressible half-spaces, even though the Bell constraint and the incompressibility constraint coincide in the isotropic infinitesimal limit.

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“…Surface waves in elastic solids were first studied by Lord Rayleigh [1885] for an isotropic elastic solid. The extension of surface wave analysis and other wave propagation problems to anisotropic elastic materials has been the subject of many studies; see, for example, [Musgrave 1959;Anderson 1961;Stoneley 1963;Chadwick and Smith 1977;Royer and Dieulesaint 1984;Barnett and Lothe 1985;Mozhaev 1995;Nair and Sotiropoulos 1997;Destrade 2001a;2001b;Destrade et al 2002;Ting 2002a;2002c;2002b;Destrade 2003;Ogden and Vinh 2004]. For problems involving surface waves in a finitely deformed pre-stressed elastic solid (strain-induced anisotropy) we refer to [Hayes and Rivlin 1961;Flavin 1963;Chadwick and Jarvis 1979;Dowaikh and Ogden 1990;1991;Norris and Sinha 1995 (concerning a solid/fluid interface) ;Chadwick 1997;Prikazchikov and Rogerson 2004 (concerning prestressed transversely isotropic solids); Destrade et al 2005;Edmondson and Fu 2009]; see also [Song and Fu 2007].…”

Section: Introductionmentioning

confidence: 99%

Propagation of waves in an incompressible transversely isotropic elastic solid with initial stress: Biot revisited

Ogden

Singh²

2011

J. Mech. Mater. Struct.

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In this paper, the general constitutive equation for a transversely isotropic hyperelastic solid in the presence of initial stress is derived, based on the theory of invariants. In the general finite deformation case for a compressible material this requires 18 invariants (17 for an incompressible material). The equations governing infinitesimal motions superimposed on a finite deformation are then used in conjunction with the constitutive law to examine the propagation of both homogeneous plane waves and, with the restriction to two dimensions, Rayleigh surface waves. For this purpose we consider incompressible materials and a restricted set of invariants that is sufficient to capture both the effects of initial stress and transverse isotropy. Moreover, the equations are specialized to the undeformed configuration in order to compare with the classical formulation of Biot. One feature of the general theory is that the speeds of homogeneous plane waves and surface waves depend nonlinearly on the initial stress, in contrast to the situation of the more specialized isotropic and orthotropic theories of Biot. The speeds of (homogeneous plane) shear waves and Rayleigh waves in an incompressible material are obtained and the significant differences from Biot's results for both isotropic and transversely isotropic materials are highlighted with calculations based on a specific form of strain-energy function.

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Some New Ideas in the Theory of Surface Acoustic Waves in Anisotropic Media

Cited by 28 publications

References 9 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

Surface waves in deformed Bell materials

Propagation of waves in an incompressible transversely isotropic elastic solid with initial stress: Biot revisited

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