Variational analysis of the reflection of surface waves by arrays of reflecting strips

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Abstract
A system of approximate surface wave equations and edge conditions in one scalar variable is derived from Hamilton’s principle for linear piezoelectric media by assuming suitable depth behavior and integrating with respect to depth. The assumed behavior with depth is determined from the known surface-wave solutions of the three-dimensional equations for both the plated and unplated substrate. The influence of the inertia, stiffness, and electrical shorting of the film is included in the analysis. The approximate equations are expressed in terms of the known fundamental material constants and no measurement of model parameters is required. Bulk-wave scattering is not considered. The approximate equations, which admit of a transmission-line representation, are applied in the analysis of surface-wave reflection by both uniformly and nonuniformly spaced arrays of reflecting strips plated on various substrates. Among other things, the calculated reflection curves indicate a slight asymmetry for heavier film materials on account of the dispersion caused by the strips. Although this effect has been observed experimentally, it has not been reproduced by other analytical models.

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