Analysis of surface instability in an elastic anisotropic cone by the use of surface waves of weak discontinuity

Abstract

The problem of surface instability of a right circular hexagonal cone is investigated. The surface of the cone is free from stresses, but in the near-surface layer initial constant tensile or compressive stresses act in the hoop direction and in the direction of the cone’s generators. Surface instability is analyzed by the use of weak nonstationary disturbances which propagate along the conic surface in the form of the nonstationary Rayleigh wave polarized in the sagittal plane and the nonstationary wave of the ‘‘whispering gallery’’ type polarized perpendicular to the sagittal plane. The analysis is carried out using the theory of discontinuities based on the conditions of compatibility; in so doing the velocities of surface wave propagation and their intensities have been obtained. It has been found that the characteristics of nonstationary Rayleigh waves and surface waves of the ‘‘whispering gallery’’ type are very sensitive to the level of the tensile or compressive stresses in the near-surface layer of an elastic cone. These properties allow one to use these types of surface waves for the analysis of surface instability of elastic bodies and for nondestructive testing of residual stresses in the vicinity of surfaces of different bodies. [Work supported by RFBR.]