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Alves, Carlos J. S.

Numerical simulations on resonance poles – the trapping case of two plane cracks. (English) Zbl 0955.76083

J. Comput. Appl. Math. 111, No. 1-2, 267-279 (1999).
Summary: We give a proof of the existence of acoustic resonance poles with Robin boundary conditions. The analysis of the elastic crack scattering problem allows us to distinguish two types of resonance poles – normal or tangential, and we present some numerical results based on a variational boundary element method. Considering two plane cracks, we also present some estimates to justify the difference between simulation results when the cracks lay on the same plane or on different ones, including a trapping case.

Cited in 3 Documents

MSC:

76Q05 Hydro- and aero-acoustics
74M15 Contact in solid mechanics
74R10 Brittle fracture
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

Keywords:

elastic wave; acoustic wave; crack shape; existence of acoustic resonance poles; Robin boundary conditions; elastic crack; scattering; variational boundary element method; trapping
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References:

[1] C.J.S. Alves, T. Ha Duong, Numerical experiments on the resonance poles associated to acoustic and elastic scattering by a plane crack, in: G. Cohen (Ed.), Mathematical and Numerical Methods for Wave Propagation, SIAM, Philadelphia, PA, 1995, pp. 544-553.; C.J.S. Alves, T. Ha Duong, Numerical experiments on the resonance poles associated to acoustic and elastic scattering by a plane crack, in: G. Cohen (Ed.), Mathematical and Numerical Methods for Wave Propagation, SIAM, Philadelphia, PA, 1995, pp. 544-553. · Zbl 0874.73077
[2] Alves, C. J.S.; Ha Duong, T., Numerical resolution of the boundary integral equations for elastic scattering by a plane crack, Int. J. Numer. Methods. Eng., 38, 2347-2371 (1995) · Zbl 0835.73066
[3] C.J.S. Alves, T. Ha Duong, On the far field amplitude for elastic waves, in: E. Meister (Ed.), Modern Mathematical Methods in Diffraction Theory and its Applications in Engineering, Peter Lang, Frankfurt, 1997, pp. 49-67.; C.J.S. Alves, T. Ha Duong, On the far field amplitude for elastic waves, in: E. Meister (Ed.), Modern Mathematical Methods in Diffraction Theory and its Applications in Engineering, Peter Lang, Frankfurt, 1997, pp. 49-67. · Zbl 0893.73019
[4] Boström, A.; Eriksson, A. S., Scattering by two penny-shaped cracks with spring boundary conditions, Proc. Roy. Soc. London A, 443, 183-201 (1993) · Zbl 0922.73012
[5] R. Dautray, J.L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 4, Masson, Paris, 1988.; R. Dautray, J.L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 4, Masson, Paris, 1988. · Zbl 0749.35003
[6] Eriksson, A. S., Natural frequencies of a penny-shaped crack with spring boundary condition, J. Appl. Mech., 62, 59-63 (1995) · Zbl 0823.73016
[7] Ha Duong, T., On the boundary integral equations for the crack opening displacement of flat cracks, Integral Equations Oper. Theory, 15, 427-453 (1992) · Zbl 0753.45005
[8] Ikawa, M., On the poles of the scattering matrix for two strictly convex obstacles, J. Math. Kyoto Univ., 23, 127-194 (1983) · Zbl 0561.35060
[9] Lax, P. D.; Phillips, R. S., On the scattering frequencies of the Laplace operator, Comm. Pure Appl. Math., 25, 85-101 (1972) · Zbl 0236.35036
[10] R.S. Phillips, On the exterior problem of the reduced wave equation, Proceedings of the Symposium in Pure Math., Vol. 23, AMS, Providence, USA, 1973, pp. 153-160.; R.S. Phillips, On the exterior problem of the reduced wave equation, Proceedings of the Symposium in Pure Math., Vol. 23, AMS, Providence, USA, 1973, pp. 153-160. · Zbl 0261.35022
[11] O. Poisson, Calcul des pôles de résonance associés à la diffraction d’ondes acoustiques et élastiques en dimension 2. Thèse de doctorat, Université de Paris IX Dauphine, 1992.; O. Poisson, Calcul des pôles de résonance associés à la diffraction d’ondes acoustiques et élastiques en dimension 2. Thèse de doctorat, Université de Paris IX Dauphine, 1992.
[12] Steinberg, S., Meromorphic families of compact operators, Arch. Rational Mech. Anal., 31, 372-380 (1968) · Zbl 0167.43002
[13] Wei, M.; Majda, G.; Strauss, W., Numerical computation of the scattering frequencies for acoustic wave equations, J. Comput. Phys., 75, 345-358 (1988) · Zbl 0643.65080
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