Frequency spectra of resonant vibration in disk plates of PbTiO3 piezoelectric ceramics

Abstract

The frequency spectra of resonant vibration in disk plates of PbTiO3 piezoelectric ceramics were observed for diameter to thickness ratio (r) of 5 to 30 near the fundamental thickness extensional mode. The observed spectra could be classified into three groups of thickness mode and two groups of radial mode. For comparison, theoretical spectra for isotropic disk plate were also calculated for various Poisson's ratios (σ) of disk material on the basis of Gazis and Mindlin's theory. The calculations showed that the theoretical radial mode spectra can be divided into a strongly σ-dependent group and a slightly dependent one, and also showed that the upper ends of terrace-type spectra appear as a straight line at the cutoff frequency in a large-r region and may be corresponded to the thickness extensional mode. In fact, the fitting of the upper-end spectra to the experimental thickness extensional mode by adjusting σ, gives not only qualitative agreement of all experimental spectra with the theoretical ones, but also the best quantitative agreement with the strongly σ-dependent theoretical spectra. Thus, all observed spectra can be predicted nearly completely from the theory of isotropic disk plate by selecting a suitable equivalent σ which is 0.18 for the present anisotropic disk.