Wentzel–Kramers–Brillouin solution of cut-off frequency for horizontal shear (SH) waves in various inhomogeneous thin films

The Wentzel–Kramers–Brillouin method is employed to study the cut-off frequencies of the horizontal shear waves in a freestanding functionally graded piezoelectric–piezomagnetic material film with the electrically and magnetically open boundary conditions. An analytical solution, which could be used in analyzing the problems of various functionally graded materials, is proven to have high precision by analytical analysis and a numerical example. The results reveal that the set of cut-off frequencies is a series of approximate arithmetic progressions. A theoretical foundation based on the relationship between the cut-off frequencies and the materials’ gradient property is established for nondestructive evaluation.