Scattering from impedance gratings and surface wave formation

The scattering problem of acoustic plane waves from comb-like impedance gratings on a rigid surface has been investigated in this paper. A rigorous analytic approach for homogeneous plane-wave incidence is presented based on the periodicity of the grating structure, in which the problem was solved as a mixed boundary value problem and the scattered field was represented by the tangent velocity difference across a partition wall of the grating. A singular integral equation has been derived for the tangent velocity difference, which can directly be solved with the Gauss-Chebyshev procedure. The resulting solution consists of a series of Bloch-Floquet waves (plane bulk wave and surface wave modes) with explicit expressions for the expansion coefficients. When the grating period is much less than the incident wavelength (ka