Abstract
Using the method of integral equations, we solved the plane problem of diffraction of elastic waves on a periodic system of rigid tunnel inserts. The obtained system of singular integral equations was solved numerically by the method of mechanical quadratures. We present the diagrams of stress distribution near the insert tips.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. G. Popov, “Interaction of plane elastic waves with systems of radial defects,” Izv. Ross. Akad. Nauk, Mekh. Tverdogo Tela, No. 4, 118–129 (1999).
A. M. Nazarenko and L. A. Fil’shtinskii, “Interaction of stress waves with rigid inserts in a half-space (plane deformation),” Izv. Akad. Nauk SSSR, Mekh. Tverdogo Tela, No. 4, 95–102 (1985).
V. F. Emets, G. S. Kit, and Ya. I. Kunets, “Asymptotic behavior of the solution of the problem of scattering of an elastic wave by a thin-walled foreign inclusion,” Izv. Ross. Akad. Nauk, Mekh. Tverdogo Tela, No. 3, 55–64 (1999).
N. A. Lavrov, Equations of the Dynamics of a Thin Inclusion in an Elastic Medium [in Russian], Preprint No. 91, Institute of Science of Machines (1993).
V. V. Panasyuk, M. P. Savruk, and Z. T. Nazarchuk, Method of Singular Integral Equations in Two-Dimensional Problems of Diffraction [in Russian], Naukova Dumka, Kiev (1984).
A. N. Guz’, V. D. Kubenko, and M. A. Cherevko, Diffraction of Elastic Waves [in Russian], Naukova Dumka, Kiev (1978).
Author information
Authors and Affiliations
Additional information
__________
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 2, pp. 94–99, March–April, 2007.
Rights and permissions
About this article
Cite this article
Nazarenko, O.M., Lozhkin, O.M. Plane problem of diffraction of elastic harmonic waves on periodic curvilinear inserts. Mater Sci 43, 249–255 (2007). https://doi.org/10.1007/s11003-007-0028-x
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11003-007-0028-x