Investigation of the dynamic behavior of a finite crack in the functionally graded materials by use of the Schmidt method

In this paper, the dynamic behavior of a finite crack in the functionally graded materials subjected to the harmonic stress waves is investigated by means of the Schmidt method. By use of the Fourier transform and defining the jumps of the displacements across the crack surfaces as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the crack length, the circular frequency of incident wave and the materials constants upon the stress intensity factor of the crack.