Dynamic behavior of a crack in a functionally graded piezoelectric strip bonded to two dissimilar half piezoelectric material planes

The dynamic behavior of a crack in a functionally graded piezoelectric material (FGPM) strip bonded to two half dissimilar piezoelectric material planes subjected to combined harmonic anti-plane shear wave and in-plane electrical loading was studied under the limited permeable and permeable electric boundary conditions. It was assumed that the elastic stiffness, piezoelectric constant and dielectric permittivity of the functionally graded piezoelectric layer vary continuously along the thickness of the strip. By using the Fourier transform, the problem can be solved with a set of dual integral equations in which the unknown variables are the jumps of the displacements and the electric potentials across the crack surfaces. In solving the dual integral equations, the jumps of the displacements and the electric potentials across the crack surfaces were expanded in a series of Jacobi polynomials. Numerical results illustrate the effects of the gradient parameter of FGPM, electric loading, wave number, thickness of FGPM strip and electric boundary conditions on the dynamic stress intensity factors (SIFs).