Air-gap determination of the cut-off frequency of unelectroded plates and effects of local thickness modifications in plane resonators

A method is proposed for obtaining precise measurements of the cutoff frequencies of unelectroded plates. These quantities can then be used in a model, similar to that which has permitted the extraction of the cutoff frequency, to determine the other parameters of the resonator (electrode geometry and mass loading). Two successive applications of these models permit one to remove most of the uncertainties relative to the material constants and to obtain precise values of the equivalent scheme and, if necessary, a response free from anharmonic modes. A model of the resonators with embedded electrodes proposed by T.J. Lukaszek (1971) has been constructed and the properties of this type of resonators computed. The models made for the three types of resonators described here are based on the approximate equations governing the thickness vibrations of piezoelectric plates established by H.F. Tiersten and coworkers (1979). Two methods of resolution of these equations were used: a semialgebraical one and the finite-elements method