Mathematik und Physik ZAMP On diraction in a piezoelectric medium by a half-plane: The Sommerfeld problem

Abstract. This paper is concerned with the diraction problem in a transversely isotropic piezoelectric medium by a half-plane. The half-plane obstacle considered here is a semi-innite slit, or a crack; both its surfaces are traction free and electric absorbent screens. In a generalized sense, we are dealing with the Sommerfeld problem in a piezoelectric medium. The coupled diraction elds between acoustic wave and electric wave are excited by both incident acoustic wave as well as incident electric wave; and the sound soft and electric \blackness " conditions on the screens are characterized by a system of simultaneous Wiener-Hopf equations. Closed form solutions are sought by employing special techniques. Some interesting results have been obtained, such as mode conversions between acoustic wave and electric wave, novel diraction patterns in the scattering elds, and the eect of electroacoustic head wave, as well as of surface wave|Bleustein-Gulyaev wave. Unlike the classical Sommerfeld problem, in which the only concern is the scattering eld of electric wave, the strength of material, e.g. material toughness, is another concern here. From this perspective, relevant dynamic eld intensity factors at the crack tip are derived explicitly