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Scattering of a sound wave by a two-sided sandwich membrane

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MWSW01 - Canonical scattering problems

Scattering of a sound plane wave by an infinite thin structure is considered. The structure is composed of a semi-infinite two-sided sandwich membrane perforated on one side and a semi-infinite acoustically hard screen. On the perforated and continuous sides, the velocity potential satisfies the first order Leppington and third order membrane boundary conditions, respectively. Two ways of applying the Fourier transforms to the boundary value problem lead to distinct governing systems of two Wiener-Hopf functional equations. It is shown that both Wiener-Hopf problems share the same characteristic polynomial and elliptic surface but reduce to different genus-1 scalar Riemann-Hilbert problems. The associated Jacobi inversion problem is solved in terms of the genus-1 Riemann theta function. Exact formulas for the Wiener-Hopf matrix factors are presented. The solvability of the problem and the discontinuity of the solution at the screens junction are discussed.

This talk is part of the Isaac Newton Institute Seminar Series series.

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