TY - JOUR

T1 - Acoustic scattering by a semi-infinite angular sector with impedance boundary conditions

AU - Lyalinov, Mikhail A.

PY - 2018

Y1 - 2018

N2 - In this work we study the problem of diffraction of an acoustic plane wave by a semi-infinite angular sector with impedance boundary conditions on its surface. It is studied by means of incomplete separation of variables. With the aid of Watson–Bessel integral representation the problem is reduced to a boundary value problem on the unit sphere with an operator-impedance boundary condition on a cut of the sphere. The latter problem is further studied by means of the traditional methods of extensions of sectorial sesquilinear forms. The Sommerfeld integral representation is obtained from that of Watson–Bessel with the aim to develop the far-field asymptotics. Analytic properties of the corresponding Sommerfeld transformant are also discussed. For a narrow impedance sector, an asymptotic formula for the diffraction coefficient of the spherical wave propagating from the vertex is derived.

AB - In this work we study the problem of diffraction of an acoustic plane wave by a semi-infinite angular sector with impedance boundary conditions on its surface. It is studied by means of incomplete separation of variables. With the aid of Watson–Bessel integral representation the problem is reduced to a boundary value problem on the unit sphere with an operator-impedance boundary condition on a cut of the sphere. The latter problem is further studied by means of the traditional methods of extensions of sectorial sesquilinear forms. The Sommerfeld integral representation is obtained from that of Watson–Bessel with the aim to develop the far-field asymptotics. Analytic properties of the corresponding Sommerfeld transformant are also discussed. For a narrow impedance sector, an asymptotic formula for the diffraction coefficient of the spherical wave propagating from the vertex is derived.

KW - Diffraction by an impedance sector

KW - Diffraction coefficient

KW - Integral representations

KW - Narrow cone

KW - diffraction by an impedance sector

KW - diffraction coefficient

KW - narrow cone

KW - QUARTER-PLANE

KW - integral representations

KW - DIFFRACTION COEFFICIENTS

KW - CONE

KW - WAVE SCATTERING

UR - http://www.scopus.com/inward/record.url?scp=85044662727&partnerID=8YFLogxK

U2 - doi:10.1093/imamat/hxx044

DO - doi:10.1093/imamat/hxx044

M3 - Article

VL - 83

SP - 53

EP - 91

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

SN - 0272-4960

IS - 1

ER -