ANTI-PLANE HARMONIC PROBLEMS FOR A CLASS OF ELASTIC MATERIALS WITH FUNCTIONAL INHOMOGENEITY

摘要

Two dynamical (harmonic) problems for an isotropic elastic media with spatially varying functional inhomogeneity are considered: the propagation of surface anti-plane shear SH waves, and the stress deformation state of an anti-plane vibrating medium with a semi-infinite crack. The shear modulus and mass density are assumed to be functions of depth into a half-space. In the shear wave problem the existence conditions and the speed of propagation of surface shear waves has been found. In the crack problem the asymptotic expression for the stress near the crack tip is analysed, which leads to a closed form solution of the dynamic stress intensity factor.