A Study Based Upon Variational Principle Of The Properties Of Surface Acoustic Waves Propagating Under Periodic Metal Grating

Originated from the equation of fluctuation and the boundary conditions and based on D.P,Chen and Haus theory, a variational principle was used to investigate surface acoustic waves passing through piezoelectric crystal with short-circuited gratings. Analyzing strip reflection coefficient produced by mechanic loading, we discovered Closed-form expressions of it for different crystal symmetry class are not uniform. With detailed deduction of closed-form expressions of the different crystal symmetry classes, we put forward, for the first time, the closed-form expressions of strip reflection coefficients of tetragonal 4/mmm, hexagonal 6/mmm and trigonal 3m crystal etc.We extended D.P,Chen and Haus theory for general Rayleigh-type SAWs to SH-type SAWs and hence discussed the dispersion characteristics of SH-type SAWs propagating on periodic metallic grating structures by means of Abbott's COM equation and Plessky's COM equation. Solution to dispersion relation of SH-type SAWs is obtained and a new approach for the theoretical analysis and design of SH-type SAWs devices has been developed.Using COM theory, the physical meaning of the dispersion relation derived from D.P,Chen and Haus theory was explained, i.e. this relation stands for the upper edge or the lower edge of the stopband,The problem of a double integral in D.P,Chen and Haus theory is transformed into that of two-dimensional finite element by virtue of Poynting theorem. Consequently, finite element method is successfully applied to analysis on reflection characteristics of metallic gratings with finite thickness in D.P,Chen and Haus theory.To apply D.P,Chen and Haus theory to the discussion of SAW propagation in periodic metallic grating structures with two fingers per period, we have studied the electrostatic problem of this gratings. Closed-form expressions for the scattered Floquet components perturbed by double-electrode gratings are given. Namely, Datta's theory for the electrostatic field of single-electrode gratings is extended to that of double-electrode gratings .Effectiveness of the above theoretical analysis is demonstrated with results of the numerical analysis for the Rayleigh SAW modes and SH-type SAW modes.This paper extends and develops D.P,Chen and Haus theory. The variational method for SAW propagation in piezoelectric crystal now can be applied to not only Rayleigh SAW modes but also SH-type SAW modes. In addition, it can be used to analyze the effects of grating with finite electrode thickness and the properties of double-electrode gratings. The authors hope that this variational method will arouse peoples's attentions because of previous study and our works and play more important role in the SAW research in future.