Band gaps of lamb waves in one-dimensional piezoelectric composite plates: effect of substrate and boundary conditions.

We theoretically study the band structures of Lamb waves in one-dimensional phononic crystal plates consisting of piezoelectric ceramics placed periodically in epoxy with epoxy or piezoelectric ceramic substrate by the virtual plane wave expansion method. The dependences of the widths and starting frequencies of first band gaps (FBG) on the substrate's thickness, the filling fraction, and the lattice spacing are calculated for different materials of substrate under different electric boundary conditions, i.e., short circuit (SC) and open circuit (OC). The FBG width decreases gradually as the substrate's thickness increases and the FBG starting frequency increases progressively as the thickness increases on the whole. The FBG widths and starting frequencies with SC are always larger than with OC. Our research shows that it is possible to control the width and starting frequency of the FBG in the engineering according to need by choosing suitable values of the substrate's thickness, the filling fraction, and the lattice spacing.