Abstract
The radial vibration of a radial composite tubular transducer with a large radiation range and power capacity is studied. The transducer is composed of a longitudinally polarized piezoelectric ceramic tube and a coaxial outer metal tube. Assuming that the longitudinal length is much larger than the radius, the electromechanical equivalent circuits of the radial vibration of a piezoelectric ceramic long tube and a metal long tube are derived and obtained for the first time following the plane strain theory. As per the condition of the continuous forces and displacements of two contact surfaces, the electromechanical equivalent circuit of the tubular transducer is obtained. The radial resonance/anti-resonance frequency equation and the expression of the effective electromechanical coupling coefficient are obtained. Then, the effects of the radial geometry dimension of the transducer on the vibration characteristics are analyzed. The theoretical resonance frequencies, anti-resonance frequencies, and the effective electromechanical coupling coefficients at the fundamental mode and the second mode are in good agreement with the finite element analysis (FEA) results. The study shows that when the overall size of the transducer is unchanged, as the proportion of piezoelectric ceramic increases, the radial resonance/anti-resonance frequency and the effective electromechanical coupling coefficient of the transducer at the fundamental mode and the second mode have certain characteristics. The radial composite tubular transducer is expected to be used in high-power ultrasonic wastewater treatment, ultrasonic degradation, and underwater acoustics, as well as other high-power ultrasonic fields.
Highlights
Longitudinal sandwich piezoelectric ceramic ultrasonic transducers, which are called Langevin piezoelectric composite ultrasonic transducers, are widely used in high-power ultrasound [1,2,3,4].The traditional sandwich ultrasonic transducers have the advantages of a simple structure, adjustable performance, and high electro-acoustic efficiency
In order to verify the correctness of the analytical theory, finite element analysis (FEA) is employed to simulate the vibrational modes of the transducer
In the cylindrical coordinate system, the linear piezoelectric constitutive equations of a be simplified as longitudinally polarized piezoelectric ceramic tube [32] are as follows:
Summary
Longitudinal sandwich piezoelectric ceramic ultrasonic transducers, which are called Langevin piezoelectric composite ultrasonic transducers, are widely used in high-power ultrasound [1,2,3,4]. The traditional sandwich ultrasonic transducers have the advantages of a simple structure, adjustable performance, and high electro-acoustic efficiency Their radial dimension is required to be much smaller than 1/4 wavelength so that the power capacity, radiation area, and output power of the transducers are all limited. When the longitudinal length is comparable to the radius, the piezoelectric element is mainly a hollow cylinder In this case, the vibration of the transducer is such a complex coupled vibration that there are only a few theories about it [16,17]. In order to enlarge the radiation area, improve the power capacity, and improve the equivalent circuit theory of the piezoelectric vibrator, the radial vibration of a high-power longitudinally polarized radial composite tubular transducer is studied. In order to verify the correctness of the analytical theory, finite element analysis (FEA) is employed to simulate the vibrational modes of the transducer
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