Sonic wave diffraction on scatterers in stratified medium

hvestigation of properties of fields, -acted on a system of scatterers, is an important problem of modem physics. Description of such phenomena m resonance fkequency range, where length of the wave close to the scatterers' dimensions, is possible only with a rigorous solution of corresponding diffraction problem. The significant difficulties arise while the scattered field is calculated in the case of an arbitrary scatterers' geometry. One of the ways to solve the problem of scalar sonic wave difEaction on scatterers in stratified medium is proposed below. Let the plane xOy forms the medium interface between coating (sonic wave velocity c1 and medium densitypl) and air. The plane y=-dis interface between coating and substrate with sonic wave velocity cz and medium density p,. A system of cylindrical W t e l y thin cracks with cross-section of L , k=m is arbitrary situated in the strip parallel to Oz-axis. We assume the arcs L, are the Lyapunov type contours of arbitrary curvature. Two-dimensional own mode of structure (time dependence exp(-iot)) with a scalar component (in plane xOy) excites the presented structure. The appeared =action problem is reduced to find the solution of twodimensional Helmholtz equation, that satisfies conditions: of continuity of pressure and normal component of velocity vector on the lower plane; of absence of waves propagated fiom infinity (except exciting one); of Dirichlet on the arcs L, k = n and on the upper plane; of M e h e r type near the scatterers' ribs (Lk arc end-points). Green h c t i o n method is used and a solution of initial problem is presented as siagle layer potential. Satismg condition on scatterers' contours the problem is reduced to system of integral equations that is salved by the mechanical quadrature method as Nazarchuk [l]. Note, the kernels of integral equations consist Sommerfeld type integrals and their calculation should be carem. For that purpose we propose to modify the integration path to avoid integrand oscillations at far zone. Taking into account we consider an own mode excitation, we introduce the coefficients of transmission, reflection and calculate dissipation energy that is dissipated in lower halfspace. Thus obtained Green function of the problem and its behaviour investigation at far zone allow us to solve effectively the problem and to enhance the solution to explore numerically the problem for wide range of its parameters.