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

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 k₀a ≈ 1 the DSCF decreases by 14–29%, while its peak drops by only 1–5%. The kernel parameters A and α dominate, while β 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%.