Three-dimensional coupled vibration theory for the longitudinally polarized piezoelectric ceramic tube

• Study 3D coupled vibration for longitudinally polarized piezoelectric ceramic tube.
• The analytical resonance frequency equation of 3D coupled vibration is obtained.
• Its vibrational distribution is simulated by using ANSYS software.

Longitudinally polarized piezoelectric ceramic devices have been widely used in underwater sound and ultrasonic transducers. When the geometrical dimensions satisfy certain conditions, the vibration can be regarded as one-dimensional vibration, such as the longitudinal vibration of a slender ceramic rod, or the plane radial vibration of a thin piezoelectric ring. However, for the longitudinally polarized piezoelectric ceramic tube with comparable longitudinal and radial geometrical dimensions, because of its complexity, its coupled vibration has not been studied up to now. In this paper, based on three-dimensional (3D) motion equations and electrostatic charge equation, according to the free boundary conditions of the piezoelectric tube, the analytical resonance frequency equation of longitudinal–radial coupled vibration for the longitudinally polarized piezoelectric tube is obtained. Its vibrational distribution is simulated by using ANSYS software. The results show that the analytical resonance frequencies are in good agreement with the numerical results and the piezoelectric tube vibrates in radial and longitudinal directions. So, it is expected that this theory can serve as reference for the design of the longitudinal–radial composite vibrational systems.