High-frequency extensional vibrations of piezoelectric ceramic bars polarized in the longitudinal direction

The approximate 1-D governing equations for coupled length-extensional, width-stretch, and symmetric width-shear vibration modes in rectangular finite piezoelectric bars with 6 mm hexagonal symmetry are presented. The bars polarized in the longitudinal direction with electrodes on the faces perpendicular to the length are considered. The system of equations is used to study the frequency spectrum of piezoelectrically forced vibrations of bars made of hard ceramics. The influence of the width-to-thickness ratio on the resonance frequency is discussed. The computed values are compared with experimental data. The material constants used for numerical simulations of resonant frequencies were obtained from the measurements on APC 841 PZT ceramics samples.