Dispersion of thickness vibrations of piezoceramic disk resonators

A piezoceramic wafer polarized and excited in its thickness direction can vibrate in thickness-longitudinal (TL) as well as thicknessshear (TS) modes of vibration which are coupled. The dispersion spectrum of a circular disk resonator is derived from the constitutive equations and evaluated for two different ceramics. As a result small deviations in material parameters can be shown to cause a conversion of the spectrum with an apparent interchange of modes. From this it can be concluded that energy trapping critically depends on some material coefficients which may be combined in a figure of merit for TL-resonator materials. This figure is relevant to the design of ceramic trapped energy devices.