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As a critical component of ultrasonic vibration systems, piezoelectric transducers play an essential role in various practical application scenarios. Recent advances in spherical transducers have been widely used in underwater sound and structural health monitoring, while the cascaded spherical piezoelectric transducer with arbitrary piezoceramic shell thickness has not been investigated. Here, we propose a radially cascaded spherical piezoelectric transducer (RCSPT) and derive its electromechanical equivalent circuit with mechanical losses, dielectric losses, and load mechanical impedances. The resulting device is composed of three concentric spherical metal shells and two radially polarized spherical piezoceramic shells. The underlying physical mechanism is the inverse piezoelectric effect, which converts electrical signals into mechanical vibrations. The effects of the spherical piezoceramic shell's thickness and location on the RCSPT are studied. We also analyze the effects of mechanical losses, dielectric losses, and load mechanical impedances on the modulus of input electric impedance of the cascaded spherical transducer. The experiments are conducted to verify the electromechanical characteristics of the resulting device, which are in good agreement with the simulated results and theoretical predictions. Our methodology will offer new possibilities for designing RCSPTs and may promote applications in various fields, such as underwater acoustic detection and structural health monitoring. [ABSTRACT FROM AUTHOR]

In this work, a functionally graded spherical piezoelectric transducer (FG-sPET) is proposed and an accurate theoretical model is constructed, mainly composed of a three-port electromechanical equivalent circuit model (EECM). The EECM of FG-sPET can be connected to that of other vibration systems according to the boundary conditions (force and vibration velocity), making it easier to evaluate the whole mechanical vibration system. The validity of the EECM for FG-sPET is verified by comparison with other literature. The effects of geometric dimensions and non-uniform coefficients on the vibration characteristics (resonance/anti-resonance frequencies and effective electromechanical coupling coefficient) of FG-sPET are also studied, contributing to systematically evaluating the key factors determining the vibration characteristics of FG-sPET. The proposed analytical system is of excellent guidance for the structural optimization design of functionally graded piezoelectric devices. [ABSTRACT FROM AUTHOR]

Electromechanical equivalent circuit of the radially polarized cylindrical piezoelectric transducer in coupled vibration is obtained. The equivalent elasticity method is used to analyze the coupled vibration. It is an approximate analytical method, ignoring the shear and torsion stresses and strains, dividing the coupled vibration into the extensional radial and longitudinal vibrations. A mechanical coupling coefficient is introduced to connect these two equivalent vibrations. According to the electromechanical equivalent circuit, the resonance frequency equations as functions of the frequency and the mechanical coupling coefficient are acquired. The sound pressure level and far field sound pressure distribution for the transducer in water are simulated. It is demonstrated that the radiation range of the cylindrical transducer is larger than that of the ring-type transducer. Several prototypes of the transducer are fabricated; the radial and longitudinal resonance frequencies are measured. The experimental resonance frequencies are in good agreement with the analytical results. The acquisition of the electromechanical equivalent circuit contributes to analyzing the electromechanical characteristics of the radial polarized cylindrical transducer. [ABSTRACT FROM AUTHOR]

Highlights • A radially composite cylindrical piezoelectric transducer consisting of a piezoelectric ceramic cylinder and the inside and outside concentric metal cylinders is analyzed. • Equivalent elasticity method is used to study the coupled vibrations of the cylinders. The electromechanical equivalent circuit is deduced, which provides a theoretical basis for the transducer in practice applications. • When the radius is comparable with the height of the transducer, the radial vibrational displacement is close to the longitudinal vibrational displacement, where the coupling between the radial vibration and the longitudinal vibration is strong. • The greater is the proportion of the piezoelectric cylinder in the transducer, the smaller are radial and longitudinal resonance frequencies, and the larger are effective electromechanical coupling coefficients. • COMSOL-Multiphysics 5.3 is employed to simulate the vibration mode and the displacement distribution of the transducer. The measured resonance frequencies of the transducer are consistent with the simulated and theoretical results. Abstract Electromechanical equivalent circuit for the radially composite cylindrical piezoelectric transducer in coupled vibration is deduced. The transducer is composed of a piezoelectric cylinder sandwiched by two concentric metal cylinders. Equivalent elasticity method is used to study the coupled vibrations of the three cylinders. A ratio named the mechanical coupling coefficient is introduced to divide the coupled vibration into the radial and longitudinal vibrations. The electromechanical equivalent circuits for the transducer and the resonance frequency equations are obtained. When the height is close to the radius of the transducer, the coupling between the radial vibration and the longitudinal vibration is strong. The thicker is the piezoelectric cylinder, the larger is the effective electromechanical coupling coefficient. Several prototypes of the transducer are fabricated. It is demonstrated that the theoretical resonance frequencies are in good agreement with the numerical and experimental results. [ABSTRACT FROM AUTHOR]

Three-dimensional coupled vibration of the composite cylindrical piezoelectric transducer is analyzed. The composite cylindrical piezoelectric transducer consists of an inner axially polarized piezoelectric ceramic cylinder and an outer metal cylinder with the same height. Coupled vibration of the composite cylindrical piezoelectric transducer is analyzed by equivalent elasticity method, which is an approximate analytical approach. According to this method, coupled vibration of the cylindrical transducer is regarded as an interaction between a plane radial vibration and a longitudinal vibration. The radial and longitudinal electromechanical equivalent circuits of the piezoelectric transducer are acquired. Input impedances as functions of the resonance frequency and the mechanical coupling coefficient are derived to obtain resonance frequency equations. The analytical results are supported by experimental and numerical simulated results of two prototypes of the piezoelectric transducer. The composite cylindrical piezoelectric transducer presented in this paper is superior to single cylindrical piezoelectric transducers, composite ring-type, and tube-type transducers in the field of high output power and efficiency. [ABSTRACT FROM AUTHOR]

• An active radial ultrasonic horn with adjustable performance is proposed. • The active adjustment of resonance frequency and displacement magnification is performed. • The ability of inductance to modulate the resonance frequency and displacement magnification is greater than that of resistance and capacitance. As a key component of high-powered ultrasonic vibration systems, ultrasonic horns play an important role in various practical application scenarios. Recent advances in longitudinal ultrasonic horns have enabled them to magnify the Langevin transducer's mechanical vibration and efficiently transmit the mechanical vibration to the mechanical load. However, limited research has been devoted to active radial ultrasonic horns in radial vibration. Here we propose an electric impedance-controlled active radial ultrasonic horn (ARUH) capable of tuning both resonance frequency and displacement magnification in radial vibration. The resulting device consists of a radially polarized piezoelectric ring connected with adjustable electric impedance and two metal rings with variable sections. The underlying mechanism is that the change of the converted mechanical impedance of the piezoelectric material by the external electric impedance connected to the piezoelectric material modulates the resonance frequency and displacement magnification of the ARUH. It can be found that the resonant frequency shifts to higher frequencies as the resistance increases and the resonant frequency shifts to lower frequencies as the inductance and capacitance increase, while the displacement magnification has the opposite trend to the resonance frequency. For example, the resonance frequency of the constant-section radial horn is 41130.2 Hz. When the inductance increases from −0.007 to 0.007H, the resonance frequency shifts from 41171.3 to 34606.2 Hz and the displacement magnification moves from 1.189 to 3.5. The experiments are conducted to verify the effectiveness of the resulting device, which is in good agreement with the simulated results and theoretical predictions. Our design with functionality and flexibility opens up possibilities for the design of ARUHs and may find important application prospects in diverse fields such as cold-drawn steel tubes and ultrasonic plastic welding. [ABSTRACT FROM AUTHOR]

A new type of ring-type piezoelectric ceramic transformer in radial vibration is studied. It is composed of two concentric piezoelectric ceramic thin rings polarized axially and radially. Based on the electromechanical equivalent circuit, when the dielectric loss of the piezoelectric ceramic materials and the mechanical contacting loss between the input and the output piezoelectric rings are taken into account, the electromechanical characteristics of the piezoelectric transformer are studied. The dependence of the voltage gain, the power gain, or the efficiency (the ratio of the output power over the input power) and the effective electromechanical coupling coefficient on the geometrical dimensions are analyzed. Meanwhile, the load dependence of the electromechanical parameters of the transformer is also investigated. Some prototypes of the piezoelectric transformers are designed and made. The resonance/antiresonance frequency and the voltage gain are measured. It is shown that the measured electromechanical parameters are in good agreement with the theoretical results. The conclusions can be used for the optimization design of the ring-type piezoelectric ceramic transformers in the engineering applications. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a semi-analytical method is proposed to investigate the transmission band gaps of Lamb waves through repetitive structures in a waveguide. For a unit cell the scattering matrix is obtained by the Lamb mode matching technique at each artificially sliced interface and then substituted into the Bloch theorem to solve the eigenproblem incurred by cell repetition. The method is implemented on a ribbed plate. The band gaps in the dispersion curves are confirmed by the dips of Lamb wave transmission coefficients, and attributed to the coupled vibrations of Lamb modes in different sliced sections of the unit cell. [Copyright &y& Elsevier]

Abstract: Based on the theory of plane strain problem, the radial vibration of the radially poled piezoelectric ceramic long tubes with arbitrary wall thickness is studied. The exact analytical theory is developed and the exact solutions for the radial displacement and the electrical potential are obtained. The three-port electro-mechanical equivalent circuit of the piezoelectric ceramic tube in radial vibration is obtained. Based on the circuit, the electric admittance is obtained and the resonance/anti-resonance frequency equations are given analytically. The relationship between the resonance/anti-resonance frequency and the geometrical dimension is analyzed. For comparison, numerical method is used to simulate the radial vibration of the piezoelectric tube. Meanwhile, some radially polarized piezoelectric ceramic tubes are designed and manufactured and the resonance/anti-resonance frequencies are measured. It is shown that the analytical resonance/anti-resonance frequencies are in good agreement with those from the numerical method. [Copyright &y& Elsevier]

Abstract: Based on the exact analytical theory, the radial vibration of an isotropic circular ring is studied and its electro-mechanical equivalent circuit is obtained. By means of the equivalent circuit model, the resonance frequency equation is derived; the relationship between the radial resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions, the material property is analyzed. For comparison, numerical method is used to simulate the radial vibration of isotropic circular rings. The resonance frequency and the radial vibrational displacement distribution are obtained, and the radial radiation acoustic field of the circular ring in radial vibration is simulated. It is illustrated that the radial resonance frequencies from the analytical method and the numerical method are in good agreement when the height is much less than the radius. When the height becomes large relative to the radius, the frequency deviation from the two methods becomes large. The reason is that the exact analytical theory is limited to thin circular ring whose height must be much less than its radius. [Copyright &y& Elsevier]

Abstract: This paper presents a new high power ultrasonic (HPU) radiator, which consists of a transducer, an ultrasonic horn, and a metal circular ring. Both the transducer and horn in longitudinal vibrations are used to drive a metal circular ring in a radial–axial coupled vibration. This coupled vibration cannot only generate ultrasound in both the radial and axial directions, but also focus the ultrasound inside the circular ring. Except for the radial–axial coupled vibration mode, the third longitudinal harmonic vibration mode with relative large vibration amplitude is also detected, which can be used as another operation mode. Overall, the HPU with these two vibration modes should have good potential to be applied in liquid processing, such as sonochemistry, ultrasonic cleaning, and Chinese herbal medicine extraction. [Copyright &y& Elsevier]

Abstract: An improved cymbal transducer with a combined piezoelectric ceramic ring and metal ring is presented and analyzed. The cymbal transducer is composed of metal caps in flexural vibration, a piezoelectric ceramic ring and a metal ring in radial vibration. The radial vibration of the radial combination of a piezoelectric ring and a metal ring is analyzed and its electro-mechanical equivalent circuit is obtained. By means of numerical method, the relationship between the resonance/anti-resonance frequency, the effective electro-mechanical coupling coefficient and the geometrical dimensions is studied. The vibrational modes of the cymbal transducer are analyzed; the admittance–frequency curve and vibrational displacement distribution are given. Two cymbal transducers are designed and manufactured, and their frequency characteristics are measured. It is shown that the simulated resonance/anti-resonance frequencies and the admittance curve of the cymbal transducer are in good agreement with the measured results. The improved cymbal transducer is expected to be used in high power underwater sound projector and ultrasonic radiators in air and liquid. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the plane radial vibration of an isotropic metal thin circular rings is studied and its equivalent circuit model is obtained. Based on the equivalent circuit model, the step-type circular ring concentrator consisting of two metal thin circular rings in radial vibration is analyzed. Its compound equivalent circuit is derived and the resonance frequency equation is obtained. The relationship between the resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions is analyzed. The resonance frequency of the step-type radial concentrator is calculated based on the resonance frequency equation. For comparison, the resonance frequency of the step-type radial concentrator is also obtained by using numerical method. It is illustrated that the resonance frequencies from these two methods are in a good agreement with each other. [Copyright &y& Elsevier]

The coupled vibration of the sandwich piezoelectric transducer with a large cross-section is analyzed using an approximate analytic method. The resonance frequency equations of the transducer are derived and the effect of the geometrical dimensions on the resonance frequency is studied. It is illustrated that when the radial vibration in the transducer is considered, the vibration of the sandwich transducer becomes more complex. Apart from the longitudinal resonance frequency, the radial resonance frequency can also be obtained. For comparison, numerical methods are also used to simulate the coupled vibration; the resonance frequency and the vibrational displacement distribution are computed. Compared with one-dimensional longitudinal theory, the radial dimensions of the transducer are no longer limited because the coupled vibration is considered. Compared with numerical methods, the physical meaning of the analytic method is concise. It is illustrated that the resonance frequencies obtained from the coupled resonance frequency equations are in good agreement with those from numerical methods, and they are in better agreement with the measured results than those from one-dimensional theory. Since the radial and the coupled vibration are considered in the analysis, more resonance frequencies can be obtained. Therefore, using the coupled resonance frequency equations, the sandwich transducer with multifrequency or wide frequency bandwidth can be designed and used in ultrasonic cleaning, ultrasonic sonochemistry and other applications. 2005 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

The piezoelectric ultrasonic composite transducer, which can be used in either gas or liquid media, is studied in this paper. The composite transducer is composed of a longitudinal sandwich piezoelectric transducer, a mechanical transformer, and a metal circular plate in flexural vibration. Acoustic radiation is produced by the flexural circular plate, which is excited by the longitudinal sandwich transducer and transformer. Based on the classic flexural theory of plates, the equivalent lumped parameters for a plate in axially symmetric flexural vibration with free boundary conditions are obtained. The radiation impedance of the plate is derived and the relationship between the radiation impedance and the frequency is analyzed. The equivalent circuits for the plate in flexural vibration and the composite transducer are given. The vibrational modes and the harmonic response of the composite piezoelectric transducer are simulated by the numerical method. Based on the theoretical and numerical analysis, two composite piezoelectric ultrasonic transducers are designed and manufactured, their admittance-frequency curves are measured, and the resonance frequency is obtained. The flexural vibrational displacement distribution of the transducer is measured with a laser scanning vibrometer. It is shown that the theoretical results are in good agreement with the measured resonance frequency and the displacement distribution. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, the resonance frequency equation and expression of displacement amplitude magnifications of a full-wave barber ultrasonic horn are obtained. By discussing the relationships between the displacement amplitude magnifications and the geometrical dimensions, the optimized design of the horn for the largest magnification is proposed, which is helpful to improve the radiation power and the transfer efficiency of the acoustic energy of the ultrasonic oscillatory system. Based on the optimized design of the horn, we introduced a barbell ultrasonic transducer operated in the longitudinal full-wave vibrational model and obtained the resonance frequency equations. For comparison, the resonance frequencies of the full-wave barbell horn and the full-wave barbell transducer are also analyzed by finite element method (FEM). It is shown that the values obtained by theoretical analysis and FEM are in good agreement with experimental observations. We hope that the research of this paper is helpful for the use of the barbell horn and transducer in the applications such as ultrasonic liquid processing. [Copyright &y& Elsevier]

Abstract: A sort of tubular ultrasonic radiator used in ultrasonic liquid processing is studied. The frequency equation of the tubular radiator is derived, and its radiated sound field in cylindrical reactor is calculated using finite element method and recorded by means of aluminum foil erosion. The results indicate that sound field of tubular ultrasonic radiator in cylindrical reactor appears standing waves along both its radial direction and axial direction, and amplitudes of standing waves decrease gradually along its radial direction, and the numbers of standing waves along its axial direction are equal to the axial wave numbers of tubular radiator. The experimental results are in good agreement with calculated results. [Copyright &y& Elsevier]