Analysis on the three-dimensional coupled vibration of composite cylindrical piezoelectric transducers

Exploring the coupled vibration behavior of Cylindrical-Conical and Cylindrical-Exponential ultrasonic concentrators for efficient energy transfer

In this paper, the coupled vibration behavior of cylindrical-conical and cylindrical-exponential ultrasonic concentrators for efficient energy transfer is investigated. A theoretical model is developed to overcome the limitations of traditional one-dimensional theories that neglect the influence of height in the study of cylindrical concentrator vibration. Employing the equivalent elasticity method, the coupled vibration is considered as an interaction between longitudinal and plane radial vibrations. By establishing radial and longitudinal equivalent circuits with their corresponding input impedances, resonance frequency equations and the radial displacement amplification factor are derived. The effects of the radial thickness and the height-to-radius ratio on the characteristic parameters are presented for optimization designs. Numerical simulations are conducted to analyze vibrational modes and validate the theoretical findings. This study enhances the understanding of the vibration mechanism of cylindrical concentrators and provides valuable insights for selecting suitable cross-sections to improve performance and effectiveness in practical applications.

Multi-mode coupled vibration performance analysis of a radial-longitudinal (R-L) ultrasonic transducer

A radial-longitudinal (R-L) ultrasonic transducer is designed by compounding a piezoelectric ceramic and an outer metal ring on the central coupling cylinder of a longitudinal cascade transducer. This design is used to realize multi-mode vibration and increase the radiation range. By applying longitudinal and radial double excitation, three coupled vibration modes of the transducer are generated in the frequency range of 15-65 kHz. The coupled vibration dominated by radial vibration is regarded as the best vibration mode of this transducer. The electromechanical equivalent circuit and the resonance frequency equation of the transducer's coupled vibration are derived by using the equivalent elastic method and one-dimensional vibration theory and verified by the finite element method and experimental method. The results show that the electrical impedance frequency curves of the transducer from the three methods are consistent. The transducer is expected to be used in ultrasonic cleaning and liquid processing applications.

Three-dimensional coupled vibration of the rectangular piezoelectric ceramic stack

The three-dimensional coupled vibration of the rectangular piezoelectric ceramic stack is analyzed by adopting the equivalent elastic method, which is an approximate analytical method. When the shear stress and strain are ignored, the complex coupled vibration of the rectangular piezoelectric ceramic stack is simplified to three one-dimensional coupled vibrations by defining three mechanical coupled coefficients. The three-dimensional electromechanical equivalent circuit is established on the basis of the analysis. The resonance frequency equation which determines the vibration mode of the piezoelectric vibrator is derived and the resonance frequencies of different modes can be calculated. According to the resonance frequency equation of coupled vibration, the effects of the length, width, and thickness of the rectangular piezoelectric ceramic stack on the resonance frequency are analyzed. Three groups of the rectangular piezoelectric ceramic stack of different dimensions are made for experiments and numerical simulations. The results show that the theoretical results are in good agreement with the experimental analysis and simulation results, which provide theoretical support for expanding the application of rectangular piezoelectric vibrators.

An Original 2-D Analytical Model for Investigating Coupled Vibrations of Finite Piezoelectric Resonators

This article deals with 2-D modeling of coupled vibrations of finite piezoelectric resonators. A general solution for all the physical quantities in the Cartesian and cylindrical coordinate systems is deduced from the governing equations by expansion in series summation of trigonometric functions of thickness coordinate and trigonometric or Bessel functions of the lateral one. The essential difference between this model and the earlier ones is that instead of expressing mainly in the thickness coordinate and integration through the thickness, the solutions are expressed in the form of double Fourier series augmented by single Fourier or Fourier-Bessel series, which contributes to better satisfy the mechanical and electrical boundary conditions. The dynamic stiffness matrix of the system is developed. Electrical impedances of a typical piezoelectric parallelepiped under stress-free and symmetrical loading conditions and its frequency spectrum for different width-to-thickness ratios are calculated using our model as well as by the finite element method. A comparison shows an excellent agreement. Finally, theoretical and measured electrical impedances of a piezoelectric parallelepiped and a piezoelectric disk are compared and discussed. The 2-D theoretical model proposed here is shown to be accurate and efficient for coupled vibration analysis of piezoelectric resonators and is applicable for any set of finite dimensions and crystal symmetry.

Modelling of a hydroacoustic projector to produce low frequency sound

Low frequency sound is useful in several underwater applications, including sonar, underwater communication, detection of mines, sonobuoys, detection of oil or gas deposits, etc. Hydroacoustic projectors help in generating such low frequency acoustic waves far more effectively than other devices. Even though there is sufficient information available on modelling of various components used in complex hydraulic devices, there is a significant dearth of literature pertaining to mathematical modelling of hydroacoustic projectors and relevant experimental data. The present work fills this gap firmly. To this end, an integrated electrical analogy-based model to simulate the behavior of a hydroacoustic projector has been developed. The model includes sub-models for a hydraulic pump, hydraulic pipelines, hydraulic cylinders, a directional control valve, an accumulator, a reservoir, mechanical mass, spring, friction, radiation impedance, and coupling elements. The model also incorporates the effects of compliance in pipelines and presence of air in the working fluid. Further, a prototype of the projector has been designed and fabricated. Predictions from simulations have been compared with experimental results from tests conducted in air up to 10 Hz frequency. These results demonstrate the reliability of the simulation model and establish its efficiency in terms of predicting the projector's performance with reasonable accuracy.

Analysis on coupled vibration of piezoelectric ceramic stack with two piezoelectric ceramic elements

A longitudinally polarized piezoelectric ceramic stack with two piezoelectric ceramic elements is an important part of sandwich piezoelectric transducers. The three-dimensional coupled vibration of piezoelectric ceramic stack is analyzed. Since the longitudinal and radial dimensions of particular piezoelectric ceramic stacks are approximately equal, one-dimensional theory cannot be used for analysis. The piezoelectric ceramic stack is analyzed by the equivalent elastic method, which is an approximate analytical method, and it is considered that the coupled vibration of a piezoelectric ceramic stack is composed of equivalent radial and longitudinal vibrations. These two equivalent vibrations are connected by a mechanical coupling coefficient. The radial and longitudinal electromechanical equivalent circuits are obtained, and the resonance frequency equations are derived. The dependency of the radial and longitudinal resonance frequencies on the geometrical dimensions for piezoelectric ceramic stack is analyzed. The height or radius has a large influence on the longitudinal resonance frequency or the radial resonance frequency. Two sets of piezoelectric ceramic stacks are fabricated. The experimental results, COMSOL simulated results, and theoretical results are in good agreement.

Electromechanical equivalent circuit of the radially polarized cylindrical piezoelectric transducer in coupled vibration

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.

Analysis of a Cascaded Piezoelectric Ultrasonic Transducer with Three Sets of Piezoelectric Ceramic Stacks

To increase the ultrasonic intensity and power of a piezoelectric transducer, a cascaded piezoelectric ultrasonic transducer with the three sets of piezoelectric ceramic stacks is analyzed. The cascaded piezoelectric ultrasonic transducer consists of four metal cylinders and three sets of piezoelectric ceramic stacks in the longitudinal direction. In analysis, the electromechanical equivalent circuit of the cascaded piezoelectric ultrasonic transducer is obtained, as well as the resonance/anti-resonance frequencies equations. By means of an analytical method, when the position of piezoelectric ceramic stacks PZT-2/PZT-3 changes, the resonance/anti-resonance frequencies and the effective electromechanical coupling coefficient of the cascaded piezoelectric ultrasonic transducer have certain characteristics. Several prototypes of the cascaded piezoelectric ultrasonic transducer are manufactured. The experimentally measured resonance frequencies are in good agreement with the theoretical and simulated results. The cascaded piezoelectric ultrasonic transducer with three sets of piezoelectric ceramic stacks presented in this paper is expected to be used in the field of high power ultrasound.

Exact series model of axially polarized hollow piezoelectric ceramic cylinders of finite length

An analytical model is presented of axisymmetric circular hollow piezoelectric ceramic cylinders with arbitrary dimensions and boundary conditions. Forced vibrations of the cylinders with specified potentials on the electroded surfaces and displacement or stress on the boundaries are considered. The exact, linearized, axisymmetric governing equations are used in the analysis. Three series solutions are used, and each term in each series is an exact solution to the exact governing equations of motion. The terms in the series expressions for components of displacement, stress, electric potential, and electrical displacement are products of Bessel and sinusoidal functions and are orthogonal to other terms. Complete sets of functions in the radial and axial directions are formed by terms in the first series and the other two, respectively. It is, therefore, possible to satisfy arbitrary boundary conditions on all surfaces of the hollow piezoelectric cylinder. Numerical results are presented for hollow piezoelectric cylinders of various dimensions. Input electrical admittance and displacements are computed for three special cases in bands that include several resonance frequencies, and they are in excellent agreement with those computed using atila-a finite element package.