Impedance Method in the Theory of Surface Waves in Inhomogeneous and Layered Media

This chapter deals with the impedance method for analysing surface waves in inhomogeneous piezoelectric structures. This analysis is based on the following arguments. We do not construct wave field solutions in the whole inhomogeneous structure by joining these fields on boundaries of irregularity, but consider only the fields on a certain convenient plane and describe the half-spaces (bordering this plane) by surface impedance matrices; the form of these matrices is defined not only by the medium character, but also by the properties of scattering inhomogeneities. This approach is quite natural because of the plane character of typical structures and allows us to split a complicated boundary-value problem of obtaining fields into two simpler independent problems: a problem of finding the surface impedances independent of fields and a problem of solving equations of motion on a plane with given impedances of adjusting half-spaces. And in this case a minimal number of variables is used for the description of both problems, and the problems themselves are posed in a compact form convenient for constructing both exact and approximate solutions by means of methods of perturbations.