On formulas for the Rayleigh wave speed

Vinh, Pham Chi; Ogden, Ray W.

doi:10.1016/j.wavemoti.2003.08.004

Cited by 71 publications

(38 citation statements)

References 4 publications

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“…Malischewsky (2000) and Vinh & Ogden (2004). It should be noted that existence and uniqueness of the Rayleigh wave have been also proved for anisotropic materials, e.g.…”

Section: Elementary Derivationmentioning

confidence: 95%

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

Kaplunov

Приказчиков

2017

Advances in Applied Mechanics

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Abstract:Explicit asymptotic formulations are derived for Rayleigh and Rayleigh-type interfacial and edge waves. The hyperbolic-elliptic duality of surface and interfacial waves is established, along with the parabolic-elliptic duality of the dispersive edge wave on a Kirchhoff plate. The effects of anisotropy, piezoelectricity, thin elastic coatings, and mixed boundary conditions are taken into consideration. The advantages of the developed approach are illustrated by steady-state and transient problems for a moving load on an elastic half-space.

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“…Malischewsky (2000) and Vinh & Ogden (2004). It should be noted that existence and uniqueness of the Rayleigh wave have been also proved for anisotropic materials, e.g.…”

Section: Elementary Derivationmentioning

confidence: 95%

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

Kaplunov

Приказчиков

2017

Advances in Applied Mechanics

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“…Legendre-Gauss-Lobatto quadrature (34). Note that the inner product in (33) involves the C tensor in the product of the strains.…”

Section: Spectral Discontinuous Galerkin Schemementioning

confidence: 99%

“…The coefficients A 1 and A 2 are not uniquely determined but instead satisfy An explicit derivation of the Rayleigh wave speed may be found in [34].…”

Section: Rayleigh Wavementioning

confidence: 99%

A high-order discontinuous Galerkin method for wave propagation through coupled elastic–acoustic media

Wilcox

Stadler

Burstedde

et al. 2010

Journal of Computational Physics

232

205

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“…The total number of particles equals 10,324, and the smoothing length in each zone equals 1.5 . The Rayleigh wave speed, C R , in the material can be obtained by first finding the largest root, η max , of the cubic equation [34] f (5.9) and then using…”

Section: One Central Crack In a Platementioning

confidence: 99%

Search algorithm, and simulation of elastodynamic crack propagation by modified smoothed particle hydrodynamics (MSPH) method

Batra

Zhang

2006

Comput Mech

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We first present a nonuniform box search algorithm with length of each side of the square box dependent on the local smoothing length, and show that it can save up to 70% CPU time as compared to the uniform box search algorithm. This is especially relevant for transient problems in which, if we enlarge the sides of boxes, we can apply the search algorithm fewer times during the solution process, and improve the computational efficiency of a numerical scheme. We illustrate the application of the search algorithm and the modified smoothed particle hydrodynamics (MSPH) method by studying the propagation of cracks in elastostatic and elastodynamic problems. The dynamic stress intensity factor computed with the MSPH method either from the stress field near the crack tip or from the J-integral agrees very well with that computed by using the finite element method. Three problems are analyzed. One of these involves a plate with a centrally located crack, and the other with three cracks on plates's horizontal centroidal axis. In each case the plate edges parallel to the crack are loaded in a direction perpendicular to the crack surface. It is found that, at low strain rates, the presence of other cracks will delay the propagation of the central crack. However, at high strain rates, the speed of propagation of the central crack is unaffected by the presence of the other two cracks. In the third problem dealing with the simulation of crack propagation in a functionally graded plate, the crack speed is found to be close to the experimental one.

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On formulas for the Rayleigh wave speed

Cited by 71 publications

References 4 publications

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

A high-order discontinuous Galerkin method for wave propagation through coupled elastic–acoustic media

Search algorithm, and simulation of elastodynamic crack propagation by modified smoothed particle hydrodynamics (MSPH) method

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