Scattering of harmonic anti-plane shear waves by two collinear cracks in functionally graded piezoelectric materials

In the present paper, the dynamic behavior of two collinear cracks in the functionally graded piezoelectric material (FGPM) is investigated. It is assumed that the elastic moduli, piezoelectric constant, dielectric permittivity and mass density of the FGPM vary continuously as an exponential function, and that FGPM is under the anti-plane mechanical loading and in-plane electric loading. By using Fourier transform and defining the jumps of displacement and electric potential across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement and electric potential across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of material properties on the stress and electric displacement intensity factors.