The scattering of SH waves by a finite crack with a superposition based diffraction technique

The problem of diffraction of cylindrical and plane SH waves by a finite crack is revisited -- We construct an approximate solution by the addition of independent diffracted terms -- We start with the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of generalized wedge -- This building block is then used to compute the diffraction of the main incident waves -- The interaction between the opposite edges of the crack is then considered one term at a time until a desired tolerance is reached -- We propose a recipe to determine the number of required interactions as a function of frequency -- The solution derived with the superposition technique can be applied at low and high frequencie

GENERAL PHYSICS – ACOUSTIC WAVES ACOUSTIC INTERACTION BETWEEN TWO CLOSE ELASTIC SPHERICAL SHELLS �

The acoustic scattering by two close thin spherical shells in water is studied. At low frequency, the resonant behavior of one shell is due to the propagation of the A-wave. The energy of this wave lies mainly in the surrounding water, so that it can easily couple two spheres, provided they are close enough. As the backscattered form function of the system composed of the two spheres is compared to that of one single sphere, a strong resonant coupling is exhibited in the low frequency region. Key words: acoustics, multiple scattering, elastic spheres, resonant coupling. 1. ACOUSTIC SCATTERING BY TWO SPHERES Let us suppose a harmonic plane wave incident on a system of two spheres embedded in water. This wave propagates in the (x, z) plane, under angle α with respect to the Oz axis. Fig. 1 shows the geometry of the problem. The observer P has coordinates (r, θ, ϕ) in the main coordinates system centered on O. Supposing an e –iωt time dependence of all acoustic fields that will be omitted throughout the paper, the displacement potential of the incident plane wave at point P may be written as ϕ = eik⋅r = eikrsin αsin θcosϕeikr cosαcosθ = with n inc standing fo