Vol. 37 No. 3 (2026): July - September
2026-09-30
Open Access

Diffraction of an SH wave by a filled elliptic cylinder in a viscoelastic medium

R.A. Sabirova

Received: 2026-10-13

Published: 2026-09-30

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Abstract

Diffraction of a time-harmonic SH wave by a filled elliptic cylinder in an unbounded viscoelastic medium with the Rzhanitsyn–Koltunov
kernel is studied; the unfilled cavity is analysed first. The freezing method reduces the problem to a Helmholtz equation with a complex
wavenumber, solved exactly in Mathieu functions of complex parameter. The algorithm is verified against the static limit, the circular-cavity
solution and the method of fundamental solutions (agreement to 10−12). Normalising the decaying incident wave at the origin overstates
the dynamic stress concentration factor (DSCF) by up to 27%; normalisation at the point of first contact is proposed. The viscous effect
is split into softening, which shifts the DSCF spectrum to lower frequencies by 37–45%, and damping, which reduces the DSCF by up to
15%. Near ????0???? ≈ 1 the DSCF decreases by 14–29%, while its peak drops by only 1–5%. The kernel parameters A and ???? dominate, while
???? has little effect (below 1.5%). For a viscoelastic filler, the ratio of filler and medium viscosities governs the stress state: the interface
stress at a stiff filler varies from −15% to +17%, the tangential stress at a soft filler from −17% to +24%.

Keywords

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About the Authors

R.A. Sabirova
r.sabirova@tkti.uz
Tashkent Chemical-Technological Institute

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How to Cite

Diffraction of an SH wave by a filled elliptic cylinder in a viscoelastic medium. (2026). Uzbek Journal “Problems of Mechanics”, 37(3). https://pmjournal.uz/jour/article/view/23

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