Application of the Reciprocity Theorem to Scattering of Surface Waves by a Surface Crack in Viscoelastic Material

Abstract

In this paper, the scattered surface waves created by a surface crack in a homogeneous, isotropic, viscoelastic half space within a plane strain condition was studied. The amplitude of the scattered surface wave in the far field was determined by using the reciprocity theory and a virtual surface wave. It was shown that the amplitude of the scattered surface wave was related to the crack-opening displacement and the crack length. In the special case of low frequency and low viscosity, the tractions due to the incident surface wave applying on the crack surface can be regarded as uniform, and a finite element method (FEM) based on rubber material was performed to verify the theoretical results. It was shown that the numerical results were consistent with the theoretical solutions, which proves the reliability of the theoretical analysis. The reciprocity theorem avoids complex integral transformation and reveals the relationship between the scattered surface wave and the size of the surface crack, which is promising in the characterization of surface cracks.

Keywords

• surface crack
• scattered surface wave
• reciprocity theorem
• crack length and depth