An interface crack between two dissimilar functionally graded piezoelectric/piezomagnetic material half infinite planes subjected to the harmonic anti-plane shear stress waves

In this paper, the dynamic behavior of an interface crack between two dissimilar functionally graded piezoelectric/piezomagnetic material half infinite planes subjected to the harmonic anti-plane shear stress waves is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with coordinate vertical to the crack. By using the Fourier transform technique, the problem can be solved with the help of a pair of dual integral equations in which the unknown variable is the jump of displacements across the crack surfaces. These equations are solved by using the Schmidt method. The relations among the electric filed, the magnetic flux field and the dynamic stress field near the crack tips can be obtained. Numerical examples are provided to show the effect of the functionally graded parameter and the circular frequency of the incident waves upon the stress, the electric displacement and the magnetic flux intensity factors of the crack.