Book excerpt: The equations of three-dimensional linear piezoelectricity are applied in the analysis of trapped energy resonators with rectangular electrodes vibrating in coupled thickness-shear and thickness-twist in the vicinity of the fundamental and odd overtone thickness-shear frequencies. Closed form asymptotic expressions for the frequency wavenumber dispersion relations for the fundamental and odd overtone coupled thickness-shear and thickness-twist waves near cutoff are obtained for both the electroded and unelectroded regions of the trapped energy resonator. The influence of piezoelectric stiffening, electrode mass loading and electrical shorting is included in the analysis. Simple approximate boundary conditions at a junction between an electroded and unelectroded region of the plate are obtained in a manner exhibiting the natural limitations inherent in the approximation.