Quasi-periodic surface Green´s dyad of a piezoelectric half-space

We present a complete computation of the surface x₁-periodic piezoelectric Green´s function based on the asymptotic decomposition method and Poisson´s summation formula. Spectral poles associated to surface acoustic waves render plane waves as expected. Behavior at small speed - large slownesses - portrays an oscillatory decay along the transversal direction while logarithmic singularities show up for longitudinal wave-numbers close to zero. At the sagittal plane, singularities arise from the periodic excitation, in accordance to previous 2-D models. Finally, we discuss the fast computation of series and future improvements.