Scattering of acoustic waves by a periodic array of elastic strips

Abstract

The scattering of a time harmonic plane wave in a fluid incident on an infinite periodic array of thin elastic strips is studied. The strips are coplanar and perpendicular to the plane of incidence. The acoustic displacement potential in the fluid is expressed as a Floquet wave expansion. Mindlin's theory of the bending of thin plates is applied to relate the pressure difference across the elastic strips to the motion of the strips. The shear and bending components of the strip motion are expanded in trigonometric basis functions, such that the shear force and bending moment are zero at the edges of the strips. The expansion coefficients are solved from the linear equations obtained by applying the method of weighted residuals to the boundary conditions on the strips and in the gaps. Anomalous reflection is observed when the incident wave frequency coincides with the transverse resonance frequencies of the strips. Resonance frequencies are observed in close pairs, corresponding to the strip resonant modes...