Dynamic behavior of a finite crack in functionally graded materials subjected to plane incident time-harmonic stress wave

In the present paper, the dynamic behavior of a finite crack in functionally graded materials subjected to normally incident elastic time harmonic waves is investigated by means of the Schmidt method. By use of the Fourier transform and defining the jumps of the displacement 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 displacement across the crack surfaces are expanded in a series. Numerical examples are provided to show the effect of the gradient parameter βa, the crack configuration on the dynamic intensity factors of cracked functionally graded materials.