Interaction of oneperiodic compliant disk ellipticshape inclusions under the action of an incident elastic time-harmonic wave

Abstract

Normal incidence of the plane elastic time-harmonic longitudinal wave on an array of coplanar thinwalled compliant elliptical inclusions having a one-periodic distribution in the 3D infinite matrix is considered. The elastic properties of inclusions are described by linear dependences between the displacement jumps and stresses in the domains of their localization. The corresponding symmetric wave scattering problem is reduced to a boundary-value integral equation for the displacement jump across the inclusion surfaces in a unit cell by means of periodic Green's function, which is presented in the form of Fourier integrals to improve the convergence of its calculations. The equation is correctly solved by using the mapping method. The frequency dependences of the mode-I stress intensity factor in vicinities of the inclusion front points for different mutual orientations in the system of elliptic inclusions are revealed. The situation with a oneperiodic array of elliptic cracks is considered as a particular case.