Quasi-Periodic Surface Green's Dyad of a Piezoelectric Half-Space
Résumé
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 wavenumbers 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.