Abstract
Coupled vibration of a radially polarized piezoelectric cylindrical transducer is analyzed with the mechanical coupling coefficient method. The method has been utilized to analyze the metal cylindrical transducer and the axially polarized piezoelectric cylindrical transducer. In this method, the mechanical coupling coefficient is introduced and defined as the stress ratio in different directions. Coupled vibration of the cylindrical transducer is regarded as the interaction of the plane radial vibration of a ring and the longitudinal vibration of a tube. For the radially polarized piezoelectric cylindrical transducer, the radial and longitudinal electric admittances as functions of mechanical coupling coefficients and angular frequencies are derived, respectively. The resonance frequency equations are obtained. The dependence of resonance frequency and mechanical coupling coefficient on aspect ratio is studied. Vibrational distributions on the surfaces of the cylindrical transducer are presented with experimental measurement. On the support of experiments, this work is verified and provides a theoretical foundation for the analysis and design of the radially polarized piezoelectric cylindrical transducer.
Highlights
Polarized piezoelectric cylindrical transducers are widely used for filters, sensors, transmitters, and actuators, as well as in the field of nondestructive testing, medical diagnostics, underwater signaling, and ultrasonic motors [1,2,3,4,5]
For the theoretical analyses of the piezoelectric cylindrical transducer, Shuaijun Wang studied the ring-type and tube-type piezoelectric transducers polarized in the radial direction [6,7]
The vibration of the piezoelectric ring is along the plane radial direction, and the vibration of the piezoelectric tube is along the longitudinal direction
Summary
Polarized piezoelectric cylindrical transducers are widely used for filters, sensors, transmitters, and actuators, as well as in the field of nondestructive testing, medical diagnostics, underwater signaling, and ultrasonic motors [1,2,3,4,5]. When the thickness of the wall of the piezoelectric transducer is without limitation, the shell and the membrane theory are not recommended In this case, the vibration of the piezoelectric cylindrical transducer is a complex coupled vibration, and the radial, circumferential, and axial stresses and strains are all considered. To analyze the complex coupled vibration of the transducer, Giebe and Blechshmidt firstly proposed that vibration of the cylindrical transducer was considered as a dynamical coupling between two partial partial mechanical mechanicalsystems systems[17] This thought provided effective to study thought provided an an effective wayway to study the the coupled vibration of large dimension andfinite finitelength lengthcylindrical cylindricaltransducers. Fewer researchers have studied thepiezoelectric radially polarized piezoelectric cylindrical transducer coupling coefficient method.
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