On discontinuity waves in linear piezoelectricity

The propagation of piezoelectric waves in an anisotropic inhomogeneous linear piezoelectric body is studied. A singular (smooth) surface or discontinuity surface of order r in the displacement and electrical fields is referred to as a weak (piezoelectric) wave if r ≥ 2 and a strong (piezoelectric) wave if r = 0, 1. It is shown that the local propagation condition for weak waves of any given order and for strong waves of order 1 can be expressed in terms of an acoustic tensor, which does not depend on r and coincides with the tensor used for plane progressive waves in the homogeneous case [see A. C. Eringen and G. A. Maugin, Electrodynamics of continua. I, Springer, New York, 1990; MR1031714 (90k:73001)(p. 488)]. For any r ≥ 1 singular hypersurfaces are characteristic for the linear piezoelectric system, whereas for r = 0 singular hypersurfaces may be non-characteristic for such equations. A condition is written which characterizes the strong waves of order 0 that are characteristic. For the latter waves the afore-mentioned acoustic tensor can be used to express the local propagation condition.