Crossing characteristics of lamb wave modes in [001]c and [011]c polarized Pb(Mg1/3Nb2/3)O3-PbTiO3 crystal plates

Multiple crossings of Lamb modes found in [001]c and [011]c polarized (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT, x=0.33 and 0.29, respectively) plates have been studied by comparing their slowness patterns with their dispersion patterns. Multiple bandgaps and crossings of Lamb wave dispersion curves are directly related to the multivalued curves in region II, and a pair of complex conjugate b2 values in region I of their slowness curves. An expression composed of elastic and piezoelectric constants has been derived to judge whether S0 and A0 modes cross with each other. This expression can be greatly simplified for non-piezoelectric materials, and there are no crossings of Lamb modes for isotropic materials.