Propagation of shear horizontal (SH) waves in a functionally graded piezoelectric substrate with periodic gratings

Propagation characteristics of SH waves in a functionally graded piezoelectric material (FGPM) substrate with periodic gratings have been investigated in the article. The material constants of the FGPM substrate change exponentially along the thickness direction. An effective numerical root finding method is adopted to solve the dispersion equation of SH waves in the complex-value domain and the theoretical results are verified by the finite element method. Effects of the material properties and height of the gratings as well as the gradient coefficient of the FGPM substrate on band structures of SH waves are investigated in detail. Numerical results show that more SH surface modes are trapped in the gratings when the shear wave velocity in the gratings decreases. The surface modes are converted into the bulk modes by tuning the negative gradient coefficient. A new low-frequency band gap is opened and SH modes with high frequencies are trapped in the gratings completely by transforming the propagating modes into the resonant modes induced by the positive gradient coefficient. The results in the article provide a theoretical foundation for designing surface acoustic wave devices with high performance based on FGPMs.