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Gomilko, A. M.; Savitsky, O. A.; Trofimchuk, A. N.

doi:10.1023/a:1014692925506

Cited by 1 publication

(3 citation statements)

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“…The solutions for the case of axial symmetry were discussed in the works of Halpern & Christiano (1986), Seimov et al (1990) and Molotkov (2002a,b). A closed form Cagniard solution (Aki & Richards 2002) was derived for the transient response problems in the high-frequency limit in the work of Paul (1976) and, for the case of a fluidporous solid interface, by Feng & Johnson (1983).…”

Section: Introductionmentioning

confidence: 99%

“…Surface or poroelastic Rayleigh waves were studied extensively in a series of works by Deresiewicz, e.g. Deresiewicz & Rice (1962); results for the fluid-porous solid interface can be found in the works of Feng & Johnson (1983; high-frequency limit) and Gubaidullin et al (2005; general case). Purely numerical results can be found, for example, in the works of Mesgouez et al (2005; finite-element formulation) and Schanz & Struckmeier (2005; boundary-element formulation).…”

Section: Introductionmentioning

confidence: 99%

“…Purely numerical results can be found, for example, in the works of Mesgouez et al (2005; finite-element formulation) and Schanz & Struckmeier (2005; boundary-element formulation). Asymptotic results for the contact stresses can be found in the work of Gomilko et al (2002).…”

Section: Introductionmentioning

confidence: 99%

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Poroelastic acoustic wave trains excited by harmonic line tractions

Gerasik

Stastna

2007

Proc. R. Soc. A.

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A two-dimensional boundary-value problem for a porous half-space with an open boundary, described by the widely recognized Biot's equations of poroelasticity, is considered. Using complex analysis techniques, a general solution is represented as a superposition of contributions from the four different types of motion corresponding to P1, P2, S and Rayleigh waves. Far-field asymptotic solutions for the bulk modes, as well as near-field numerical results, are investigated. Most notably, this analysis reveals the following: (i) a line traction generates three wave trains corresponding to the bulk modes, so that P1, P2 and S modes emerge from corresponding wave trains at a certain distance from the source, (ii) bulk modes propagating along the plane boundary are subjected to geometric attenuation, which is found quantitatively to be x K3/2 , similar to the classical results in perfect elasticity theory, (iii) the Rayleigh wave is found to be predominant at the surface in both the near (due to the negation of the P1 and S wave trains) and the far field (due to geometric attenuation of the bulk modes), and (iv) the recovery of the transition to the classical perfect elasticity asymptotic results validates the asymptotics established herein.

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Section: Introductionmentioning

confidence: 99%