Spherical Piezoelectric Transducer Research Articles

Radial vibration analysis for piezoceramic shell-stacked spherical transducer with thick walls

With the development of ultrasonic transducers, spherical piezoelectric transducers have attracted tremendous attention in a variety of application fields due to their ability to resist higher pressures and produce omnidirectional radiation. However, the wall thickness of piezoceramic spherical shells is usually thin due to the limitations of polarization technology and operating voltage, leading to the limited vibration performance and power capacity of the spherical transducer. We present a piezoceramic shell-stacked spherical transducer (PSST) capable of addressing the problem of difficult excitation caused by the thick wall of the piezoceramic shell. The resulting device consists of a two-layered piezoceramic shell interposed between the inner and outer concentric spherical metal shells. By removing the equivalent mechanical transformers, a novel electromechanical equivalent circuit of the PSST is established to simplify the theoretical analysis of the designed PSST. The electromechanical characteristics of the resulting device are experimentally verified, and the measured results are in good agreement with the theoretical predictions and simulation results. Our design opens up possibilities for designing spherical transducers with high-vibration performance and may offer potential for a wide range of applications such as underwater detection and structural health monitoring.

Effect of electric impedance on the electromechanical characteristics of tunable spherical piezoelectric transducer

Spherical piezoelectric transducers are a critical component of ultrasonic vibration systems with significant applications in various practical scenarios such as underwater acoustic detection and structural health monitoring. The existing spherical piezoelectric transducers have fixed electromechanical characteristics that limit their applications in scenarios with multi-frequency or frequency variation requirements. It would therefore be intriguing, from the viewpoints of both science and technology, to break through this limit by introducing external electric load impedance. Here we propose a tunable spherical piezoelectric transducer (TSPT) capable of adjusting the electromechanical characteristics by changing the resistance, inductance, and capacitance applied to the passive piezoceramic shell. The theoretical and numerical results show that when the resistance is exerted on the inner and outer piezoceramic shells, the resonance is accompanied by large variations at low values of resistance, while it becomes almost constant at high values of resistance. When the inductance is exerted on the outer piezoceramic shell, the resonance frequency obtained by the finite element method can be changed from 72730 Hz to 42928 Hz by adjusting the inductance, indicating that the TSPT can realize a rich and selective resonance frequency region. The resonance/antiresonance frequency decreases while the effective electromechanical coupling coefficient increases, when the capacitance applied on the inner and outer piezoceramic shells increases. The experiments are conducted to verify the effectiveness of the proposed TSPT, which is in agreement with the simulated results and theoretical predictions. Our methodology will offer possibilities to extend the working frequency range of the existing piezoelectric spherical transducer for underwater acoustic detection, hydrophones, and the spherical smart aggregate for civil structural health monitoring.

Systematic design and experimental realization of a radially cascaded spherical piezoelectric transducer.

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.

Spherical piezoelectric transducers of functionally graded materials.

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.

Design and implementation of half-space radiation high frequency broadband “spherical” transducer based on anti-sound baffle and circuit matching

In underwater acoustic communication engineering applications, it is sometimes necessary to place the communication transducers underwater. This usually requires the transducers to have the ability to radiate in half-space. At the same time, in order to reduce the transmission error rate, it is also necessary that the transducers have the ability to operate in a wide band. The spherical piezoelectric transducers have full space radiation, and high power and energy density. The design of spherical transducer by using anti-sound baffle and circuit tuning can meet the requirements of underwater communication transducers. In this work, we analyze the directivity of a spherical transducer by comparing the simulations and theoretical computations. In addition, the broadband performance of a spherical transducer is analyzed based on series inductance tuning. Finally, a half-space broadband spherical transducer prototype is manufactured and its performance is tested and verified by performing experiments. The experimental results show that the bandwidth of the spherical transducer can be increased by series inductance. Moreover, the results show that the distance from the center of the spherical transducer to the anti-sound baffle and the working frequency have a significant effect on the directivity of a spherical transducer. The test results of transducer prototype show that the directivity angle of the transducer is greater than 180°, and the operating bandwidth is around 18 kHz–54 kHz.

Spherical-Omnidirectional Piezoelectric Composite Transducer for High- Frequency Underwater Acoustics.

Spherical-omnidirectional acoustic source has become a powerful tool to provide a near-ideal omnidirectional beam pattern for acoustic tests and communications. Current spherical-omnidirectional acoustic sources do not combine an omnidirectional beam pattern with a high transmitting voltage response (TVR) in the frequency range of above 200 kHz. This work presents the design, fabrication, and measurements of a high-frequency spherical-omnidirectional transducer that can provide a near-ideal omnidirectional beam pattern and a high TVR. The active element of the transducer consists of six identical square coupons with spherical curvature 1-3 piezoelectric composites operating in thickness mode. Electroacoustic responses of the fabricated transducer in water were measured. The measured resonance frequency of the transducer was 280 kHz. The maximum TVR was 161.3 dB re 1 μ Pa/V@1 m. The horizontal and vertical beamwidths of the transducer were 360° and 346°, respectively. Measurements show that the spherical piezoelectric composite transducer has a favorable spherical-omnidirectional behavior and a high TVR at high frequency. These results demonstrate that the spherical piezoelectric composite transducer is potentially a strong candidate for a high-frequency underwater acoustic source that requires an omnidirectional response.

A novelly universal theory: Toward accurately evaluating radial vibration characteristics for radially sandwiched spherical piezoelectric transducer

With the development of ultrasonic technology, some ultrasonic processing technologies require a wide processing range. In this paper, a radially sandwiched spherical piezoelectric transducer is proposed and analyzed, which is composed of a spherical piezoelectric ceramic sandwiched by two concentric spherical metal shells. The electromechanical equivalent circuits of the spherically isotropic spherical shell and the spherical piezoelectric ceramic with arbitrary wall thickness are derived from their motion equations. According to the mechanical boundary conditions, the electromechanical equivalent circuits and frequency equation of various piezoelectric composite vibration systems can be obtained, including the radially sandwiched spherical piezoelectric transducer. The correctness of the proposed theory is verified via comparison with the finite element method and the previous theoretical model. In addition, the 2nd-order effective mechanical coupling coefficient for the radially sandwiched spherical piezoelectric transducer is higher than that of 1st-order within a specific range of wall thickness, which can be designed as the high-frequency transducer. The radially sandwiched spherical piezoelectric transducer is expected to be used in underwater sound, structural health monitoring, and high-frequency ultrasound.

An Exact and Practical Analyzing Model for Radial Vibration of Piezoelectric Spherical Transducers With Arbitrary Wall Thickness.

The piezoelectric spherical transducers have attracted extensive attention in hydroacoustics and health monitoring. However, most reported piezoelectric spherical transducers are merely analyzed by the thin spherical shell theory, which is unsuitable for the gradually increased spherical shell thickness. Therefore, it is necessary to develop the radial vibration theory of the piezoelectric spherical transducer with arbitrary wall thickness. Herein, an exact analyzing model for the radial vibration of the piezoelectric spherical transducer with arbitrary wall thickness is proposed. The radial displacement and electric potential for radial vibration of the piezoelectric spherical transducer are precisely given, and then, the electromechanical equivalent circuit is obtained. Based on the electromechanical equivalent circuit, the resonance/antiresonance frequency equations of piezoelectric spherical transducers in the radial vibration are obtained. Besides, the relationship between performance parameters and wall thicknesses is discussed. The wall thickness has a significant influence on the performance parameters of the spherical transducer. The accuracy of the theory is validated by comparing the results with the experiment and finite element analysis.

Analysis on an improved resistance tuning type multi-frequency piezoelectric spherical transducer

The existing piezoelectric spherical transducers with fixed prescribed dynamic characteristics limit their application in scenarios with multi-frequency or frequency variation requirement. To address this issue, this work proposes an improved design of piezoelectric spherical transducers using the resistance tuning method. Two piezoceramic shells are the functional elements with one for actuation and the other for tuning through the variation of load resistance. The theoretical model of the proposed design is given based on our previous work. The effects of the resistance, the middle surface radius and the thickness of the epoxy adhesive layer on the dynamic characteristics of the transducer are explored by numerical analysis. The numerical results show that the multi-frequency characteristics of the transducer can be obtained by tuning the resistance, and its electromechanical coupling coefficient can be optimized by a matching resistance. The proposed design and derived theoretical solution are validated by comparing with the literature given special examples as well as an experimental study. The present study demonstrates the feasibility of using the proposed design to realize the multi-frequency characteristics, which is helpful to improve the performance of piezoelectric spherical transducers used in underwater acoustic detection, hydrophones, and the spherical smart aggregate (SSA) used in civil structural health monitoring, enhancing their operation at the multiple working frequencies to meet different application requirements.

Underwater Spiral Wave Sound Source Based on Phased Array with Three Transducers.

This paper realizes an underwater spiral wave sound source by using three omni-directional spherical transducers with three different phases. The pressure distribution of the sound field for a phased array is derived using the superposition theory of sound field. The generation of spiral wave field is presented, the relationship between the performance of phased array sound field and the array parameters is analyzed, and also verified by the finite element method (FEM). A spiral wave sound source with three spherical piezoelectric ceramic transducers is then designed and fabricated based on FEM simulation, and the performance of the sound source is analyzed. Measurements are made in a reverberation pool, and the result shows that the fabricated spiral wave sound source is capable of producing a spiral sound wave. Under a frequency of 3.5 kHz, the phase directivity has a fluctuation of ±21°, and the amplitude directivity range is 4.3 dB, which verifies the realization of the spiral wave sound source.

Broadband Vibrational Energy Harvesting with a Spherical Piezoelectric Transducer Devoted to Underwater Wireless Sensor Networks

A new sensing node container based on a spherical piezoelectric transducer is proposed. This device provides broadband vibrational energy harvesting and sensing facilities intended for underwater wireless sensor networks. The transducer is composed of two acrylic glass (PMMA) half-spherical shells and a Pz26 piezoelectric ring clamped between the two shells. A simulation model of vibrational energy harvesting has been developed with electromechanical circuits for thickness and radial vibrational modes. This approach was validated by a finite element simulation. As a result, optimal power harvesting conditions and estimated harvested voltage were defined. A prototype of 2.2 cm in diameter was realized and characterized. Analysis in air environment reveals several structural resonance modes in the 20–80 kHz frequency range. The directivity patterns corresponding to these modes was obtained using laser Doppler vibrometry. The measurements for the underwater environment show that the structural resonance modes shift down in frequency to the 10–60 kHz range, and exhibiting low directivity dependence. Power harvesting performances was measured and quantified relative to acoustical pres- sure measurements using a hydrophone. The average conversion coefficient value was found to be in the order of 3 V/MPa. In broadband excitation mode, and for an acoustic pressure of 10 kPa, the amount of harvested power out of 5 main resonance modes is 3.3 μW.

An autonomous low-power management system for energy harvesting from a miniaturized spherical piezoelectric transducer.

A new spherical vibrational energy harvesting device with an additional low power management circuit for optimizing the power transfer from the mechanical vibrations to a storage capacitor is presented. The device is devoted to underwater wireless sensor network applications due to its broadband vibrational energy harvesting, sensing, and communicating facilities. The sensing node container consists of two acrylic glass (PMMA) half-spherical shells and a Pz26 piezoelectric ring clamped between the shells. The energy harvesting, the management circuit, and communication electronics were fitted within the hollow portion of the sphere. A simulation model of the energy extraction and management system using spice has been developed. This simulation shows the feasibility and efficiency of the low power extraction circuit; a level of the necessary stored voltage was set at 3 V. The numerical model was validated by underwater experimental measurements; a voltage of 3 V was obtained at the terminals of a storage capacitor (47 µF) which was sufficient to supply the communication electronics. Power harvesting performances were measured relative to the transmitter/sensor distance and the incident acoustical field excitation voltage. Finally, 175 µW of harvested power has been measured with an excitation voltage of 8 Vpp at 5 cm distance from the emitter.

Modeling and analysis of multilayer piezoelectric-elastic spherical transducers

An exact analytical model of multilayer piezoelectric-elastic spherical transducers is established in this article, and their dynamic characteristics are studied. Based on the linear theory of piezoelasticity, the dynamic analytical solution is derived in terms of Bessel functions, Lommel functions, Gamma functions, and Generalized Hypergeometric functions, and the electric impedance is obtained to determine the resonance frequencies. By proper selection of the layer number and geometric dimensions, the proposed model can approximately degrade into some special cases in the previous works, including single-layer piezoelectric spherical transducer, two-layer piezoelectric-elastic spherical transducer, and three-layer sandwiched piezoelectric-elastic-piezoelectric spherical transducer. Comparisons between the results of the proposed model and the ones of these special cases are also given and good agreements are found. Furthermore, parametric studies are conducted to discuss the effects of the key parameters on the dynamic characteristics of these special cases and a multilayer case, such as the first resonance and anti-resonance frequencies as well as the corresponding electromechanical coupling factor. This work contributes to an overall understanding of the dynamic characteristics of miniature piezoelectric hollow sphere transducers (BBs) and stacked piezoelectric spherical transducers. The developed model can be used to guide the design of the multilayer piezoelectric-elastic spherical transducers for promising applications in underwater acoustic detection, ultrasonic imaging, hydrophones, and nondestructive testing.

A source term approach for generation of one-way acoustic waves in the Euler and Navier–Stokes equations

We derive a volumetric source term for the Euler and Navier–Stokes equations that mimics the generation of unidirectional acoustic waves from an arbitrary smooth surface in three-dimensional space. The model is constructed as a linear combination of monopole and dipole sources in the mass, momentum, and energy equations. The singular source distribution on the surface is regularized on a computational grid by convolution with a smeared Dirac delta function. The source is implemented in the Euler equation using a Cartesian-grid finite-volume WENO scheme, and validated by comparing with analytical solution for unidirectional planar and spherical acoustic waves. Using the scheme, we emulate a spherical piezoelectric transducer and a multi-element array medical transducer to simulate focused ultrasound fields in water. The simulated ultrasound fields show favorable agreement with previous experiments.

Influence of the Oscillating Circuit on the Emission of Nonstationary Acoustic Waves by an Electroelastic Sphere

We consider the nonstationary problem of emission of acoustic waves by a thick-walled spherical piezoelectric transducer connected to a generator of electric pulses via an oscillatory circuit with concentrated parameters. The transient process is modeled by equations of the coupled theory of electroelasticity, acoustic approximation, and the quasistatic theory for the electric circuit. We propose a method with the help of which the problem is reduced to the solution of the system of Volterra integral equations with retarded arguments. On the basis of the performed numerical calculations, we estimate the influence of a wire line on the processes running in a hydroelectroelastic system.

Unidirectional multimode piezoelectric spherical transducers

Analytical and experimental results are presented for unidirectional broadband multimode piezoelectric acoustic transducers utilizing axisymmetric vibrations of spherical transducers. The analysis covers the acoustic radiation and reception by including the acoustic impedance's and diffraction coefficients for transducers with conformal baffles. The energy method is used to obtain equivalent parameters for a multi-contour electromechanical circuit representation of the transducer and to calculate performance. Experimental data obtained are in good agreement with analytical results.

Receiving sensitivity and transmitting voltage response of a fluid loaded spherical piezoelectric transducer with an elastic coating

A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.

The static response of functionally graded radially polarized piezoelectric spherical shells assensors and actuators

This paper analyzes the static response of a functionally graded spherical shell made ofpiezoelectric materials. A hollow piezoelectric sphere is polarized in the radial direction.Spherically symmetric problems of piezoelectric spherical shells as sensors or actuators areconsidered. For the gradient of power-law behavior, closed-form explicit expressions for theelectroelastic field are derived. These solutions can serve as benchmarks for functionallygraded piezoelectric hollow spheres. For arbitrarily varying gradient, an analyticapproach for reducing the problem to a Fredholm integral equation is suggested toobtain the responses of the electroelastic field. Numerical results for a sphericalpiezoelectric vessel are obtained for special radial nonhomogeneity, and the distributionof the radial and circumferential stresses as well as the response of the electricpotential for sensors and actuators are presented graphically under electrical andmechanical stimuli, respectively. Our results indicate that the gradient indexstrongly affects the stress distribution and electric response. The obtained results arehelpful for optimizing the design of hollow spherical piezoelectric transducers.

Electric to acoustic conversion by a spherical piezoceramic shell with shields

A problem of nonstationary hydroelectroelasticity is solved to determine the pressure in the ambient medium when a spherical thin-walled piezoelectric transducer with a shield either inside or outside is excited with an electric pulse

Radial vibration characteristics of spherical piezoelectric transducers

This paper presents the vibration characteristics of the radial mode in spherical piezoelectric transducers. The differential equations of piezoelectric radial motion have been derived in terms of radial displacement and electric potential. Applying mechanical and electrical boundary conditions yielded a characteristic equation for radial vibration. Theoretical calculations of the fundamental natural frequency have been compared with numerical and experimental results for transducers of several sizes, and have shown a good agreement. This paper discusses the dependence of natural frequencies on the radius and thickness of the piezoelectric spheres and the difference between piezoelectric and elastic resonances. From the results it has been concluded that the natural frequency was not affected for the first radial mode but was reduced by the piezoelectric phenomenon. It has also been concluded that the natural frequency of the first radial mode depended mostly on the radius rather than on the thickness of the sphere whereas the natural frequency of the second radial mode depended mostly on the thickness rather than the radius.