Redirective scattering cross section reduction of a cylinder: A mathematical model

Abstract

To study the modification of the scattering cross section of cylinders by periodic or aperiodic surface loading we consider scattering by a cylinder with non‐uniform boundary conditions. Exact analytical approaches lead to considerable complexity. This paper explores the use of a least squares boundary residual method [J. Brian Davies, IEEE Trans. Microwave Theory Tech. MTT‐21(2), 99–103 (1973)] to obtain the reradiated field or scattering pattern of a cylinder clad by an alternating sequence of axially directed acoustically hard and soft strips, under uniform plane wave illumination. Data will be presented with the cylinder diameter, a, the number of strips, M, the strip widths, aφn, and the relative weighting of the soft and hard boundary conditions, H, as parameters. We considered two strip cylinders with 9 ⩽ ka ⩽ 30, and a sequence of results for ka = 5, 10, 20, and 30 with 2, 4, 8, 16, and 18 strips. Single precision programming sensibly limited the number of terms, N, in our Hankel function expansion to 18 thus fluctuations on the boundary modeled by (cossin) Nφ cannot be resolved if they exceed this periodicity. Results agreed well with classical results for the hard and soft cylinder for ka = 5, 10, and with experimental results available for a slotted cylinder at ka = 5. Single precision limited us to values of 2a ≲ 9.5λ.