Circular Transducer Research Articles

Force Attenuation Properties of Padded Dance Support Socks.

Foot injuries occur frequently in dancers, and researchers have investigated different protective measures to reduce their incidence. Research has primarily focused on ballet, but foot injuries also are common in modern and contemporary dance where footwear is not worn. While padded dance socks are a potential solution, the extent to which they provide force reduction for the feet is unknown.<br/> Purpose: This study investigates the extent to which padded dance support socks can reduce force on the foot during a dance sequence and when landing from a sauté jump.<br/> Methods: Twenty-one injury-free dancers (2 M, 19 F; age: 21.5 ± 6.7 years; height: 165.5 ± 6.1 cm; mass: 68.6 ± 15.0 kg) volunteered for this randomized, cross-over design study. Participants per- formed a 40-second modern dance sequence and a sauté jump landing under two conditions: wearing Apolla Performance Shock™ dance socks (DS) and with bare feet (BF). During these activities, 1.0 cm diameter circular force transducers were affixed under the first metatarsophalangeal joint and under the center of the heel. The sensors wirelessly recorded peak toe force, peak heel force, mean toe force, and mean heel force during dancing. A force platform measured vertical ground reaction force (VGRF) and time to peak VGRF, while the foot sensors measured peak toe force and peak heel force, during the jump landings. A Noraxon MR3.12 biomechanics system synchronized and recorded the data. All force data were normalized to body weight (BW). Dependent samples t-tests were used to assess pairwise differences in these measures between the DS and BF conditions. Alpha was set at p < 0.05.<br/> Results: Mean and peak heel forces/BW when dancing with DS were significantly lower than during BF dancing (mean: p = 0.015; peak: p = 0.0004). Peak VGRF/BW when landing from the sauté jump with DS was significantly lower compared with landing in BF (p = 0.035). All other variables were not significantly different between conditions, but all DS force values were lower than BF.<br/> Conclusions: We offer evidence that padded dance socks may reduce foot forces dancers commonly encounter during modern dance. The trends we recorded require further study to assess the extent to which the socks exhibit beneficial effects when considering both the many hours dancers train and the cumulative effects of impacts sustained by their feet.

Spatiotemporal Deconvolution of Hydrophone Response for Linear and Nonlinear Beams-Part I: Theory, Spatial-Averaging Correction Formulas, and Criteria for Sensitive Element Size.

This article reports spatiotemporal deconvolution methods and simple empirical formulas to correct pressure and beamwidth measurements for spatial averaging across a hydrophone sensitive element. Readers who are uninterested in hydrophone theory may proceed directly to Appendix A for an easy method to estimate spatial-averaging correction factors. Hydrophones were modeled as angular spectrum filters. Simulations modeled nine circular transducers (1-10 MHz; F/1.4-F/3.2) driven at six power levels and measured with eight hydrophones (432 beam/hydrophone combinations). For example, the model predicts that if a 200- [Formula: see text] membrane hydrophone measures a moderately nonlinear 5-MHz beam from an F/1 transducer, spatial-averaging correction factors are 33% (peak compressional pressure or pc ), 18% (peak rarefactional pressure or p ), and 18% (full width half maximum or FWHM). Theoretical and experimental estimates of spatial-averaging correction factors to were in good agreement (within 5%) for linear and moderately nonlinear signals. Criteria for maximum appropriate hydrophone sensitive element size as functions of experimental parameters were derived. Unlike the oft-cited International Electrotechnical Commission (IEC) criterion, the new criteria were derived for focusing rather than planar transducers and can accommodate nonlinear signals in addition to linear signals. Responsible reporting of hydrophone-based pressure and beamwidth measurements should always acknowledge spatial-averaging considerations.

Transmitting Performance Simulation of Piezoelectric Transducer for Underwater Application

This paper reports transmitting performance simulation of the circular piezoelectric transducer using finite element analysis (FEA) approach. The 3D model of the transducer is designed and simulated using six different piezoelectric materials. FEA simulation and modelling had been carried out using the COMSOL Multiphysics 5.0 software. The thickness and radius of the piezoelectric material layer were varied and transmitting performance were compared and analysed. From this simulation, the transmitting performance of the Piezoelectric Micro Ultrasonic Transducer (PMUT) is decreased as the membrane radius increased, while it increased as the thickness of the piezoelectric material layer increased. The total device thickness at 430 µm with the membrane radius at 1500 µm, show the best performance at 240 kHz of frequency, tailored for many underwater applications. The thickness and radius have contributed significantly to the mechanical stress generated at the surface of the piezoelectric material layer, in contact with the electrode. Hence, the device radius and thickness of the piezoelectric layer are considered, regardless of the type of piezoelectric material used.

Evaluating elongated grains with diffuse ultrasonic double scattering and rectangular transducers.

Diffuse scattering of ultrasound by the microstructure of polycrystal specimens can be used to evaluate grain size and grain elongation. The existing diffuse scattering models mostly dealt with circular transducers whose symmetrical sound field is insensitive to the asymmetric elongated grain. The sound field of a rectangular transducer provides a new perspective for acquiring additional information. First, the existing single scattering response (SSR) and double scattering response (DSR) models are modified for a rectangular transducer, where the sound field of a rectangular transducer is equivalent to that of an elliptical transducer in the far-field. Therefore, an equivalent single Gaussian beam model is derived using amplitude-equivalent and beamwidth-equivalent coefficients. Then, the spatial correlation function of elongated grains is transformed into the wavenumber domain, giving rise to the SSR and DSR of a rectangular transducer that reveals the interaction effect of an asymmetric sound field and elongated grains on ultrasonic backscattering. The experimental results show that the sizes of elongated grains in a cold-rolled aluminum are evaluated as 1086 ± 8, 90 ± 4, and 10 ± 1 μm in the x, y, and z directions, where the exact values are 1184.2 ± 11.9, 80.7 ± 5.2, and 8.3 ± 0.5 μm according to metallographic measurements.

An integrated platform for metamaterial-based sensing and surface acoustic wave-based acoustofluidics utilising circular interdigital transducers

A key challenge in developing lab-on-a-chip devices is integrating various functionalities such as liquid manipulation and sensing on a single platform, which conventionally requires different technologies to be separately optimized.

Vibration characteristics of two-dimensional orthogonalcomposite sandwich piezoelectric circular transducer

Vibration characteristics of two-dimensional orthogonalcomposite sandwich piezoelectric circular transducer

Hydroacoustics for density and biomass estimations in aquaculture ponds

The use of hydroacoustics is currently being studied and developed as a promising non-intrusive methodology to monitor and manage fish stocks in aquaculture farms. The main objective of this study was to develop an acoustic method for the estimation of fish density and biomass in inland aquaculture farms and test the accuracy and precision of the estimates with real data provided by the company. The study was conducted in sea bass (Dicentrarchus labrax) production ponds located in Seville (Southern Spain). A Simrad EK60 echosounder with two split-beam circular transducers operating simultaneously at 200 kHz was used for hydroacoustic surveys. Two different hydroacoustic designs were considered: central trajectories and zigzag trajectories. The accuracy and precision of the estimates were examined in order to select the best sampling design. Due to a non-homogeneous fish distribution in the pond caused by the avoidance behaviour, as a response to the sampling disturbance presented by fish, acoustic density and biomass were corrected by applying sampling theory according to the probability of fish detection. When density and biomass were corrected, the estimates became highly accurate and precise with respect to real data, which confirms that the proposed method is adequate. Similarly, acoustic estimates of fish weight were highly in agreement with real data, due to the use of specific equations developed “in situ” for the study. Although no significant differences were recorded in the density and biomass estimates with regard to the trajectory used (central vs. zigzag), it was observed that the most accurate agreement and precision were always obtained in central trajectories. Therefore, central design is proposed as the most appropriate design for hydroacoustic measurements in inland ponds. The results obtained in this study provide estimates of density and biomass that accurately match the real data, supporting the use of hydroacoustics as a potentially valid tool to manage inland aquaculture farms.

Electrical admittance of a circular piezoelectric transducer and chargeless deformation effect

The electromechanical impedance (EMI) method is a promising technique for the sake of structural health monitoring. This method measures the electrical admittance of a piezoelectric transducer attached to a host structure. If the mechanical admittance of the host structure is retrieved from the measured electrical admittance, more information about the host structure can be obtained. For this purpose, an accurate analytical closed-form expression relating the electrical admittance of a piezoelectric transducer to the mechanical admittance of a host structure is needed. Although such expression is available in literature for a circular piezoelectric transducer (CPT), the authors found it erroneous. In this work, closed-form expressions of the mechanical impedance of a free CPT and the electrical admittance of a CPT attached to a host structure are re-defined. Following, the latter is validated by comparing its result with that of an experiment. Successful use of such expressions demands accurate values of the material properties of the transducer. Hereto an analytical-experimental procedure for material calibration of a CPT is proposed. Next, the procedure of detecting the natural frequencies of a host structure using the EMI method is discussed. Using 3D numerical simulations, it is demonstrated that some of the natural frequencies cannot be detected. In essence, the corresponding mode shapes of those natural frequencies impose a deformation onto a CPT which generates a non-significant electric charge.

Vibration and acoustic radiation characteristics of cylindrical piezoelectric transducers with circumferential steps

Circular cylindrical transducers have a wide range of applications in ultrasound generation. Introducing axial or circumferential stepped-thickness variations affects the performance of these transducers. This paper investigates the effect of circumferential stepped-thickness variations on the vibration and acoustic characteristics of a circular cylindrical piezoelectric shell. FEM software ANSYS is used to simulate these characteristics and experiments are performed to validate the simulations. Stress concentration levels due to these steps are observed in order to avoid exceeding the material limit. The results show that these steps can excite certain mode shapes which produce strong ultrasound fields and these modes have circumferential wave numbers commensurate with the number of stepped regions. These steps localize the vibration within the thin-walled regions leading to higher amplitude acoustic waves produced by constructive interference. Superiority of a circumferentially stepped transducer over an axially stepped one is demonstrated in this study through a much more uniform acoustic field along the length of the transducer as well as a lower frequency of operation at the intended mode shape. The effect of input excitation is also investigated and it is shown that introducing circumferential steps is more effective in terms of acoustic amplification than increasing the input excitation for the uniform-thickness transducer.

Superposition model of mode shapes composed of travelling torsional guided waves excited by multiple circular transducer arrays in pipes

In pipe inspection using ultrasonic guided wave technique, the current commercial transmitters are designed for the unidirectional guided wave excitation using multiple circular piezoelectric transducers arrays in the axial direction. However, the source with many individual transducer elements in arrays has difficulty in achieving an axisymmetric loading perfectly for defect detection. Therefore, a quasi-axisymmetric wave is formed due to many undesired wave modes are launched instead of a pure axisymmetric wave at a given excitation frequency. In this paper, a realistic superposition model of axial multiple transducer arrays is proposed. The model has many potential applications; one example is investigating the source influence on the generated quasi-axisymmetric wave effect. The analytical model is employed to achieve the predictions for investigating a transmitter’s influence for the unidirectional enhancement of torsional T(0,1) guided wave mode excitation in a pipe inspection system composing of three piezoelectric transducer ring arrays. The excitation function with variable power levels among transducers in arrays is also introduced. The predictive results using the analytical model for the distribution of circumferential displacement amplitudes over time are verified using the finite element method and a CLV-3D laser vibrometry measurement on a 219.1-mm-outer-diameter steel pipe without defect. A comparison between calculated and test results has been analysed quantitatively. The respective results are in good agreement. Thus, predictions for the superposed wavefield can be used to analyse the realistic characterisation of the excitation function in axial multiple transducer arrays. Additionally, a sensitivity analysis for part-circumferential crack detection using the quasi-axisymmetric torsional modes generated is also evaluated using finite element modelling.

Simulation of pulsed ultrasonic diffraction in viscous fluids using transmission line matrix method.

Ultrasonic fields propagating in viscous media undergo changes in shape due to diffraction, attenuation, and dispersion. Until now, some implementations in the transmission line matrix (TLM) method has been developed to simulate either diffraction or attenuation but never both. In this work, the quadratic frequency dependence of the absorption coefficient as well as the dispersive effect of a viscous fluid are introduced in the TLM method. The idea is to decompose the emitted wave into its components at different frequencies using Fourier transform. Then, dispersion and attenuation effects are considered for each wave component separately before superposing them to get the required acoustic response. This is possible because each one of them is characterized by a constant absorption coefficient and propagates at a single speed. This TLM model has been applied to the diffracted ultrasonic field by a circular transducer radiating a short pulse in a viscous fluid. The obtained waveforms are interpreted in terms of plane and edge waves. A study of the influence of the most important parameters on the waveform of the detected ultrasonic pulses is performed. The numerical results obtained highlight the attenuation effect on the waves' shapes and the influence of the dispersion on their arrival times.

Circular synthetic aperture acoustic imaging of spherical targets in cylindrical rod clutter

A model apparatus has been built to demonstrate acoustic imaging of several spherical targets in cylindrical clutter. Reflective ultrasonic tomography imaging was chosen because the medical community, using photo-acoustic tomography imaging, utilizes a similar back-projection imaging algorithm. The experiment involves suspending an ultrasonic transducer unit (resonant frequency 1.0 MHz) in an aquarium filled with water. The transducer (sender-receiver) generates a 5-cycle tone burst. The circular plane array transducer diameter is D = 1.27 cm. Its wavelength is 1.48 mm (using c = 1482 m/s). The target, located 15 cm from the source, consists of two 0.64 cm diameter metal spheres separated by 5 cm. A mechanical structure of thin perforated disks (10 cm diam) comprise a step-motor controlled rotational platform that supports the targets and slender stainless steel cylindrical vertical rods (2 mm diameter, 10 cm long) that serve as the clutter. Received echoes versus time (data sets) were measured at 10° rotation increments of the structure (from 0° to 360°) for back-projecting the 2-D image reflectance of the targets among the clutter (using Mathematica®). The original apparatus and supporting electronics were built by Madeline Bell for her USNA Capstone research (Fall 2020) involving scattering from cylindrical targets.

1.5-Dimensional Circular Array Transducer for In Vivo Endoscopic Ultrasonography.

Traditional endoscopic ultrasonography (EUS), which uses one-dimensional (1-D) curvilinear or radial/circular transducers, cannot achieve dynamic elevational focusing, and the slice thickness is not sufficient. The purpose of this study was to design and fabricate a 1.5-dimensional (1.5-D) circular array transducer to achieve dynamic elevational focusing in EUS in vivo. An 84 × 5 element 1.5-D circular array transducer was successfully developed and characterized in this study. It was fabricated with PZT-5H 1-3 composite that attained a high-electromechanical coupling factor and low-acoustic impedance. The acoustic field distribution was measured with different transmission modes to validate the 1.5-D elevational beam focusing capability. The imaging performance of the 84 × 5 element 1.5-D circular array transducer was evaluated by two wire phantoms, an agar-based cyst phantom, an ex vivo swine pancreas, and an in vivo rhesus macaque rectum based on multifocal ray-line imaging method with five-row elevational beam steering. It was demonstrated that the transducer exhibited a central frequency of 6.47 MHz with an average bandwidth of 50%, a two-way insertion loss of 23 dB, and crosstalk of <-26 dB around the center frequency. Dynamic elevational focusing and the enhancement of the slice thickness in EUS were obtained with a 1.5-D circular array transducer. This study promotes the development of multirow and two-dimensional array EUS probes for a more precise clinical diagnosis and treatment.

Experimental characterization of nonlinear static and dynamic behaviors of circular capacitive microplates with initial deflection

In this paper, the effects of initial deflection on the static and dynamic behaviors of circular capacitive transducers are experimentally investigated. The obtained results are in good agreement with numerical simulations. It is shown that the initial deflection has a major impact on the static response of the resonator by shifting the pull-in voltage, and on its dynamic response by increasing the resonance frequency and modifying the bifurcation topology from softening to hardening behavior. Moreover, the dynamic behavior of the microplate may display nonlinear periodic and quasiperiodic responses due to geometric and electrostatic nonlinearities.

Research on Array Structures of Acoustic Directional Transducer

This paper focuses on the directivity design of array structures of acoustic directional transducers. Based on Huygens principles, the directivity formula of transducer arrays under random distribution in xyz space is derived when the circular piston transducers are used as the array element, which is used to analyze the directivity and acoustic pressure of conical transducer arrangements. In addition, a practical approach to analyze the directivity and acoustic pressure of transducer arrays under random arrangements is proposed. Findings. The conical transducer arrays show side lobes at higher frequency. Below the frequency of 2 kHz, array directivity shows rapid changes. Above the frequency of 2 kHz, array directivity varies slowly with frequency. Besides, the beam width is Θ − 3 dB ≤ 29.85 ° .

Properties of PMN-PT single crystal piezoelectric material and its application in underwater acoustic transducer

In order to further understand the characteristics of PMN-PT piezoelectric single crystal materials, the piezoelectric constant d33, impedance and frequency characteristics of PMN-PT piezoelectric single crystal elements under different pressures are studied in this paper, and the performances of PMN-PT piezoelectric single crystal elements are compared with PZT-4 piezoelectric ceramic elements. The non prestressed PMN-PT piezoelectric single crystal sandwich dipole transducer is studied and compared with PZT-4 piezoelectric ceramic sandwich dipole transducer of the same size. The matching layer broadband PMN-PT piezoelectric single crystal circular composite rod transducer is studied. The stress distribution of the transducer under 10 N pressure is calculated, and the problem of local crack of the piezoelectric single crystal element is solved from the structural design. The results show that the PMN-PT piezoelectric single crystal material has obvious advantages in low frequency performance, acoustoelectric and electroacoustic conversion efficiency, and can improve the emission and reception performance of acoustic transducer at the same time. The maximum transmitting voltage response and receiving sensitivity of the non prestressed sandwich dipole transducer can reach 144 dB and −166 dB respectively. Compared with piezoelectric ceramic transducer, the resonance frequency is reduced by about 3 kHz, and the transmitting and receiving performance are improved by 3 dB and 6 dB respectively. The matching layer broadband PMN-PT piezoelectric single crystal circular composite rod transducer has a transmitting voltage response of more than 136 dB, fluctuation of less than 5 dB, receiving sensitivity of more than −176 dB and fluctuation of less than 6 dB in the frequency range from 20 kHz to 40 kHz. The research results of this paper have important reference value and guiding significance for the popularization of PMN-PT piezoelectric single crystal material and its application in acoustic transducer.

Correction for Hydrophone Spatial Averaging Artifacts for Circular Sources.

This article reports an investigation of an inverse-filter method to correct for experimental underestimation of pressure due to spatial averaging across a hydrophone sensitive element. The spatial averaging filter (SAF) depends on hydrophone type (membrane, needle, or fiber-optic), hydrophone geometrical sensitive element diameter, transducer driving frequency, and transducer F number (ratio of focal length to diameter). The absolute difference between theoretical and experimental SAFs for 25 transducer/hydrophone pairs was 7% ± 3% (mean ± standard deviation). Empirical formulas based on SAFs are provided to enable researchers to easily correct for hydrophone spatial averaging errors in peak compressional pressure ( pc ), peak rarefactional pressure ( pr ), and pulse intensity integral. The empirical formulas show, for example, that if a 3-MHz, F /2 transducer is driven to moderate nonlinear distortion and measured at the focal point with a 500- [Formula: see text] membrane hydrophone, then spatial averaging errors are approximately 16% ( pc ), 12% ( pr ), and 24% (pulse intensity integral). The formulas are based on circular transducers but also provide plausible upper bounds for spatial averaging errors for transducers with rectangular-transmit apertures, such as linear and phased arrays.

Numerical evaluation of a fractional calculus model for the spatial impulse response of a circular piston

In lossless media, exact analytical expressions for the spatial impulse response describe the effect of diffraction in the time domain for several specific transducer shapes. At present, no exact analytical expressions are available for lossy media, so numerical evaluation of the spatial impulse response is required. For attenuation that follows a power law, the spatial impulse response is numerically evaluated by superposing contributions from time-domain Green's functions for the Power Law Wave Equation, which is a fractional calculus model for power law attenuation. To demonstrate examples of lossy spatial impulse responses obtained with these time-domain Green's functions, which are expressed in terms of maximally skewed stable densities, numerical results are computed for a circular transducer using different attenuation values and compared with the analytical result for a lossless medium. The results show that the numerically computed spatial impulse response for a lossy medium converges to the analytical result evaluated in a lossless medium as the value of the attenuation constant decreases. As the attenuation constant grows larger, the temporal extent increases, and the sharp edges are replaced by increasingly smooth curves, as observed in numerical evaluations of the lossy spatial impulse response evaluated in multiple locations.

Focused acoustic vortex generated by a circular array of planar sector transducers using an acoustic lens, and its application in object manipulation

For enhanced energy utilization with improved flexibility and capability for object manipulation, a focused acoustic vortex (FAV) is devised by installing a spherical acoustic lens on a circular array of planar sector transducers. Based on the acoustic refraction of a concave spherical acoustic lens, numerical simulations show that an FAV with considerable pressure gain and strengthened acoustic gradient force (AGF) can be produced by the effective concentration of acoustic waves. The performance of rotational object trapping is shown by the axial and radial distributions of the AGF for FAVs of different orders. Elastic objects of nanometer, micrometer, millimeter, and even larger-than-wavelength size can be captured with the trapping radius determined by the topological charge. With the established 16-channel experimental system, FAVs of different orders are verified by their clear pressure circles and phase spirals. The trapping radius and rotation speed of object capture are demonstrated using polyethylene particles of various sizes and FAVs of different orders. The favorable results provide an experimentally applicable method of FAV generation using the simplified circular transducer array to accomplish more accurate, stable, and flexible object manipulations with strengthened AGFs. Also, FAVs could offer an efficient means of high-intensity focused ultrasound therapy to improve the therapeutic effect of tumor treatments by accumulating drug particles, thereby enabling more potential applications in clinical practice.

An image formation model for ultrasound superresolution using a polymer ball lens

Ultrasonic superresolution images can be generated using a polymer ball lens. Here, we provide an image formation model for this superresolution imaging method. The imaging system is comprised of a circular flat transducer operating in pulse-echo mode with a central frequency of 1MHZ, and a ball lens centered in the beam axis of symmetry. The wavelength in water is λ0=1.5mm. The system experimentally achieves a resolution of 0.6λ0 in the focal plane at one wavelength away from the lens. Finite-element simulations are performed to compute the point-spread function of the system. The obtained numerical results are remarkably consistent with experimental data. For illustration purpose, the superresolution method is compared with a conventional ultrasonic system based on a spherically focused transducer. Our technique presents twice more resolution with a shorter depth-of-field of 2λ0. Possible applications that take advantage of these features are discussed, as well as some limitations of the proposed technique.