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.

A FEM-based method using harmonic overtones to determine the effective elastic, dielectric, and piezoelectric parameters of freely vibrating thick piezoelectric disks

“…A resonance mode superimposed on an another mode was named with the main characteristic mode and an identification mode within parentheses. For example, the mode denoted TE 1 (R 6 ) has a low-frequency mode shape of the first thickness extensional mode TE 1 with a superimposed mode that has the same characteristic surface wavelength as mode R 6 [5].…”

“…The surface motion of thick piezoelectric BaTiO 3 disks with diameter to thickness ratios between 1 and 7 has been measured by an optical method in which radial, thickness extensional, and edge mode vibrations were identified [4]. The resonant frequency response of thin piezoelectric ceramic PbTiO 3 disks has been measured using a transmission circuit, showing three groups of thickness modes and two groups of radial modes [5]. The vertical vibration velocity distributions and the frequency spectra of beveled and unbeveled Pb(Zr·Ti)O 3 disks have also been measured [6].…”

Vector representation of resonators in eigencoupling state space and eigenloss state space of piezoelectric ceramics

“…Such cylinders have been studied by several authors e.g. [10], and it is found that at a certain thickness/radius ratio, strong resonance is observed. It is likely that at this ratio an eigenstate is excited, which gives rise to strong coupling over a large area in the body of the resonator.…”

Finite Element Modelling of Piezoelectric Ceramic Disks

“…Experimental studies of vibrational modes in piezoelectric ceramic disks have been reported in the literature [1,2]. Shaw [l] measured vibrational modes in thick barium titanate disks having d l t between 1.0 and 6.6.…”