Interaction of a compressional impulse with a slot normal to the surface of an elastic half space

Abstract

An improved finite difference scheme is applied to simulate wave propagation in the vicinity of a slot normal to the surface of an elastic half space. It provides visualization of the scattered wave pattern at a sequence of time steps, and also the components of displacement as functions of time at a series of observation points.After being hit by a normally incident plane P pulse, the slot oscillates with two main cycles and two shear-compressional pairs of diffracted waves, and also Rayleigh pulses, are scattered from it. The resulting wavefronts are parallel to the vertical surfaces of the slot and curve in semicircular arcs around the bottom of the slot.Experimental tests of the theory were performed, using 0.5-6 MHz ultrasonic pulses on duralumin cylinders with surface-breaking slots ranging from 0.5-2 mm in width and from 2-6 mm in depth. The numerical results were confirmed by these experiments.

Crack Characterisation in Turbine Disks

“…In parallel with the experimental studies, supporting theoretical study on pulsed compressional wave interaction with surface-breaking slots based on numerical finite-difference models has been performed (Ilan et al 1979). In the finite-difference technique a grid of nodes is imposed onto the region containing the slot and the continuous equations of motion are approximated by a centre-difference formulation.…”

“…In the numerical modelling work of Ilan et al (1979) on elastic wave scattering the configuration of a compression wave pulse incident on a surface-breaking slot was considered and the generation of strong Rayleigh waves by the crack observed.…”

Numerical particle motion of Rayleigh waves in laterally inhomogeneous media.

“…The use of the finite difference method in solving wave propagation problems has been studied extensively by Alterman and her colleagues (ALTERMAN and KARAL, 1968;LOWENTHAL and ALTERMAN, 1972). The method was later applied to solve wave propagation problems in realistic models (BOORE, 1972;MUNASINGHE and FARNELL, 1973;ALFORD et al, 1974;ILAN et al, 1979;FuYUKI and MATSUMOTO, 1980;PEREYRA et al, 1980;BOORE et al, 1981). These studies aim at body wave or Love wave problems.…”

Scattering of Plane Waves by a Partially Closed Crack

“…Let transient plane C or SV waves be incident on the semi-infinite crack at an angle e. The elastodynamic field due to the incident wave may be described by the two dimensional transient scalar potentials 0 and Y where [5] is applied to obtain a fifth order sm0othed wavelet.…”