Rectangular Transducer Research Articles

Ultrasonic field modeling for immersed components using Gaussian beam superposition

The Gaussian beam (GB) superposition approach can be applied to model ultrasound propagation in complex-structured materials and components. In this article, progress made in extending and applying the Gaussian beam superposition technique to model the beam fields generated by transducers with flat and focused rectangular apertures as well as with circular focused apertures is addressed. The refraction of transducer beam fields through curved surfaces is illustrated by calculation results for beam fields generated in curved components during immersion testing. In particular, the following developments are put forward: (i) the use of individually determined sets of GBs to model transducer beam fields with a number of less than ten beams; (ii) the application of the GB representation of rectangular transducers to focusing probes, as well as to the problem of transmission through interfaces; and (iii) computationally efficient transient modeling by superposition of ‘temporally limited’ GBs.

Long Range Inspection of Wall Reduction of Tank Utilizing Zero-th Order Symmetric Mode Lamb Wave —Performance Demonstration of the Method Proposed—

We developed a new long range inspection method of corrosion-induced wall reduction of storage tanks. The method utilizes the zero-th order symmetric mode (So-mode) Lamb waves excited and monitored by a specially designed rectangular compression type PZT transducer mounted on the edge of the annular plate and side wall. The system can measure both the location and damage depth from the arrival time and amplitude of the So-mode reflected by the defects, respectively. We first measured attenuation of the So-mode wave and then the depth of dishshaped wall reduction on single carbon steel plate. Amplitude of the So-mode wave reflected by the defects was found to increase proportionally with the defect depth less than 15% of the plate thickness (10 mm). Amplitude of the reflected So-mode Lamb wave from the shallow dishshaped defects with depth of 0.6 mm or 7.5% to the plate thickness was detected. We also detected the So-mode waves from corrosion-induced dish-shaped wall reduction with 1.45 mm depth in 10 mm plate. Artificial groove of 1 mm depth on the step-weld 8 mm plates could be detected by the proposed method. [doi:10.2320/matertrans.I-MRA2007843]

Numerical solutions of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation satisfying the Rankine-Hugoniot condition

A numerical method that solves the KZK equation and satisfies the Rankine-Hugoniot relation for shock-wave propagation is described and characterized. By comparison with a known planar solution, it is demonstrated that current numerical methods in both the time and frequency domains predict a shock front that is stationary relative to the propagation phase and that the proposed method predicts the correct speed. These methods are then compared in the context of shock-wave lithotripsy and high intensity focused ultrasound. At the focus, axisymmetric shock-wave lithotripter simulations show that the Rankine-Hugoniot method predicts peak positive pressures that are 20% smaller, peak negative pressures that are 10% larger, and a full width at half maximum that is 45% larger. High-intensity focused ultrasound simulations for an axisymmetric transducer in water have even larger variations in peak positive pressures and intensity but smaller variations in peak negative pressure. Simulations for a rectangular transducer in tissue, where absorption is more prominent, exhibit smaller but significant variations in peak pressures and intensity. Satisfying the Rankine-Hugoniot condition plays an important role in numerical simulations of the KZK equation. [This work was supported by NIH Grants R01-HL075485 and 1R01-CA114093-02.]

Prediction of Ultrasonic Signals Captured from a Side-Drilled Hole Using a Rectangular Transducer

For the proper interpretation of ultrasonic measurement results from a side-drilled hole (SDH) using a rectangular transducer, it is very helpful to have a complete ultrasonic measurement model. A highly efficient ultrasonic beam model of a rectangular transducer and an accurate scattering model of a SDH are currently available. However, to develop such a complete measurement model, a reference model for the system efficiency factor is also needed. In this study a reference model suitable for a rectangular transducer is given and combined with existing models to develop a complete ultrasonic measurement model that can the predict ultrasonic signals from a SDH. Based on this model, we have calculated the ultrasonic signals from a SDH at different transducer orientations and compared the model-based predictions with experiments.

An ultrasonic measurement model using a multi-Gaussian beam model for a rectangular transducer

To date, ultrasonic measurement models have primarily treated systems where circular transducers are used. Recently, however, a highly efficient ultrasonic beam model for a rectangular transducer has also become available where the transducer is represented as a superposition of a relatively few Gaussian beams. Thus, using the multi-Gaussian beams, we developed ultrasonic measurement models for systems where a rectangular transducer is employed. In this paper, we describe the developed models including the beam model, the efficiency factor for a rectangular transducer and far-field scattering models for some standard scatterers. Furthermore, the accuracy of the proposed model is verified by the comparison of the model-based predictions to the experimental measurements.

Food drying process by power ultrasound

Drying processes, which have a great significance in the food industry, are frequently based on the use of thermal energy. Nevertheless, such methods may produce structural changes in the products. Consequently, a great emphasis is presently given to novel treatments where the quality will be preserved. Such is the case of the application of high-power ultrasound which represents an emergent and promising technology. During the last few years, we have been involved in the development of an ultrasonic dehydration process, based on the application of the ultrasonic vibration in direct contact with the product. Such a process has been the object of a detailed study at laboratory stage on the influence of the different parameters involved. This paper deals with the development and testing of a prototype system for the application and evaluation of the process at a pre-industrial stage. Such prototype is based on a high-power rectangular plate transducer, working at a frequency of 20 kHz, with a power capacity of about 100 W. In order to study mechanical and thermal effects, the system is provided with a series of sensors which permit monitoring the parameters of the process. Specific software has also been developed to facilitate data collection and analysis. The system has been tested with vegetable samples.

The ultrasonic probe for the investigating of internal object structure by ultrasound transmission tomography

The main component of every device used for investigating internal object structure by Ultrasound Transmission Tomography (UTT) is a special ultrasonic probe. This paper presents the structure of model multielement ring probe for examining objects using this method in divergent ray projection geometry. The probe is made up of 1024 rectangular separate piezoelectric transducers working at frequency f = 1.7 MHz, placed inside a ring with diameter D = 30 cm and height h = 9 cm. Each element of the probe is equipped with a quarter-wave matching layer. All the transducers function as transmitters and receivers, and can be joined in groups both during transmitting and during receiving. Some examples of admittance characteristics of a single piezoelectric transducer and examples of shapes of pulses generated and received by particular transducers were presented. Important factors affecting the measurement resolution are the sizes of the active surface of the transducers.

Electromechanical coupling coefficient of an ultrasonic array element

One of the most important parameters for characterizing piezoelectric materials is the so-called electromechanical coupling coefficient, k, which describes the electromechanical coupling strength. Although this parameter should be an intrinsic material parameter, it appears to depend on the aspect ratio of the resonator. There are three different values defined for three extreme geometries, k33, k33′, and kt, and they differ by more than 50%. Unfortunately, these three values cannot describe resonators of general geometries and also create conceptual confusion. Here, we provide a unified formula that will accurately describe the coupling coefficient of rectangular slender bar transducer array element with any aspect ratio.

Calculation of Radiation Beam Field from Phased Array Ultrasonic Transducers Using Expanded Multi-Gaussian Beam Model

For the reliable application of ultrasonic phased array technique, it is necessary to understand the characteristics of the radiation beam field from the array transducers quantitatively. Very recently, it has been developed the expanded multi-Gaussian beam model that can calculate the radiation beam field from a single, rectangular transducer with great computational efficiency. In this paper, this model is adopted to calculate the radiation beam field from array transducers with various time delays to achieve steering and/or focusing. The calculation results are compared to those obtained by well known Rayleigh-Sommerfeld integral that provides the exact solution in order to explore the validity of the expanded multi-Gaussian beam model in this task.

Pressure field of rectangular transducers at finite amplitude in three dimensions

In this study, the nonlinear pressure fields of various sized rectangular transducers are modeled in three dimensions. The model was based on Aanonsen’s model, which has earlier been presented for circular sources. The nonlinear wave propagation at finite amplitude is presented for square and rectangular type sources up to three harmonics. Numerical results are also tested using available experimental measurements on the acoustic axis. Good agreement is shown with the experiment for both square and rectangular cases. (E-mail: oakaya@inonu.edu.tr)

An efficient calculation algorithm for focusing by plane ultrasonic transducers

In the present paper, we simulate focused wave fields generated by a system of plane transducers used in an immersion ultrasonic technique. The ultrasonic beam penetrates into the elastic medium through the fluid–solid boundary. A real-time computer algorithm is proposed to calculate stress components in the solid medium. It is shown that a good focusing wave structure can be provided by a pair of plane rectangular transducers, inclined with respect to each other and to the beam acoustic axis.

Calculation of Spatial Impulse Response for Array Transducer

Unlike the conventional method of obtaining the spatial impulse response (SIR) for a transducer from the time domain, we propose a new and computationally efficient approach for calculating the acoustic field for a rectangular focusing array transducer in a transmitting, receiving, or transmitting–receiving (pulse–echo) mode from the frequency domain. The SIR spectrum, corresponding to each single frequency, is derived by superposing the sound fields generated by the subdivided rectangular sources. The time-domain pressure variation is obtained by taking the inverse Fourier transform from the combination of each SIR spectrum for the array. The results for a single rectangular transducer in transmitting and receiving modes match well with those from previous studies. The SIR spectrum for a focusing linear array transducer with multiple field scatterers is also developed. The proposed approach markedly reduces the number of sampling points, thereby substantially increasing the computation efficiency.

Modeling of finite-amplitude sound beams: second order fields generated by a parametric loudspeaker

The nonlinear interaction of sound waves in air has been applied to sound reproduction for audio applications. A directional audible sound can be generated by amplitude-modulating the ultrasound carrier with an audio signal, then transmitting it from a parametric loudspeaker. This brings the need of a computationally efficient model to describe the propagation of finite-amplitude sound beams for the system design and optimization. A quasilinear analytical solution capable of fast numerical evaluation is presented for the second-order fields of the sum-, difference-frequency and second harmonic components. It is based on a virtual-complex-source approach, wherein the source field is treated as an aggregation of a set of complex virtual sources located in complex distance, then the corresponding fundamental sound field is reduced to the computation of sums of simple functions by exploiting the integrability of Gaussian functions. By this result, the five-dimensional integral expressions for the second-order sound fields are simplified to one-dimensional integrals. Furthermore, a substantial analytical reduction to sums of single integrals also is derived for an arbitrary source distribution when the basis functions are expressible as a sum of products of trigonometric functions. The validity of the proposed method is confirmed by a comparison of numerical results with experimental data previously published for the rectangular ultrasonic transducer.

Piezoelectric ceramic rectangular transducers in flexural vibration

Based on the equivalent elastic method and coupled vibration theory, an analytic method is presented to study the flexural vibration of rectangular transducers consisting of piezoelectric ceramic thin plates. By introducing a mechanical coupling coefficient, the flexural vibration of the piezoelectric ceramic rectangular thin plate is reduced to two simple, one-dimensional flexural vibrations of narrow piezoelectric ceramic strips. The resonance frequency equations for the piezoelectric ceramic rectangular thin-plate transducers in flexural vibration are derived under the free and simply supported boundary conditions analytically. The relationship between the resonance frequency and the flexural vibrational order, the geometrical shape, and the dimensions of the piezoelectric ceramic rectangular thin-plate transducer is analyzed. It is demonstrated that the one-dimensional vibrational theory for the flexural vibration of a narrow piezoelectric ceramic strip and the stripe-mode flexural vibrational theory for the piezoelectric ceramic rectangular thin plate can be derived directly from the theory obtained in this paper. Experimental results show that the measured resonance frequencies of the piezoelectric ceramic rectangular thin-plate transducers in flexural vibration under free-boundary conditions are in good agreement with the calculated results. The method presented in this paper can be used in the resonance frequency analysis of vibrating systems in coupled vibration.

Numerical modeling of Harmonic Imaging and Pulse Inversion fields

Tissue Harmonic Imaging (THI) and Pulse Inversion (PI) Harmonic Imaging exploit the harmonics generated as a result of nonlinear propagation through tissue to improve the performance of imaging systems. A 3D finite difference model, that solves the KZK equation in the frequency domain, is used to investigate the finite amplitude fields produced by rectangular transducers driven with short pulses and their inverses, in water and homogeneous tissue. This enables the characteristic of the fields and the effective PI field to be calculated. The suppression of the fundamental field in PI is monitored, and the suppression of side lobes and a reduction in the effective beamwidth for each field are calculated. In addition, the differences between the pulse and inverse pulse spectra resulting from the use of very short pulses are noted, and the differences in the location of the fundamental and second harmonic spectral peaks observed.

Modeling the quasicompressional wave field of a rectangular transducer in a transversely isotropic solid.

A fast model for simulating the transient quasicompressional wave field of a rectangular ultrasonic transducer directly coupled to a transversely isotropic elastic half-space of general orientation is developed. The so-called two-tier asymptotic approach and the uniform stationary phase method are used to derive the high-frequency asymptotics of time-harmonic displacements. Then, transient fields are modeled by means of harmonic synthesis. In geometrical regions, the formulas involve elementary and inside boundary layers, well-known special functions (Fresnel integral and generalized Fresnel integral), and are applicable in the radiating near field. The asymptotics elucidate the physics in terms of various arrivals and give explicit dependence of the radiated waves upon model parameters. The asymptotic code is tested against a direct numerical solution. It is at least a thousand times faster but describes accurately both arrival times and amplitudes of various pulses radiated by the transducer.

Estimation of the Length of the Near Zone of a Rectangular Transducer

The length of the near zone of a rectangular transducer is calculated directly. The results obtained are compared with formulas for calculating the length of the near zone recommended by the European Standard EN 12668-2.

Effect of absorption on nonlinear propagation of short ultrasound pulses generated by rectangular transducers

A numerical solution of the KZK-type parabolic nonlinear evolution equation is presented for finite-amplitude sound beams radiated by rectangular sources. The initial acoustic waveform is a short tone burst, similar to those used in diagnostic ultrasound. The generation of higher harmonic components and their spatial structure are investigated for media similar to tissue with various frequency dependent absorption properties. Nonlinear propagation in a thermoviscous fluid with a quadratic frequency law of absorption is compared to that in tissue with a nearly linear frequency law of absorption. The algorithm is based on that originally developed by Lee and Hamilton [J. Acoust. Soc. Am. 97, 906–917 (1995)] to model circular sources. The algorithm is generalized for two-dimensional sources without axial symmetry. The diffraction integral is adapted in the time–domain for two dimensions with the implicit backward finite difference (IBFD) scheme in the nearfield and with the alternate direction implicit (ADI) method at longer distances. Arbitrary frequency dependence of absorption is included in this model and solved in the frequency–domain using the FFT technique. The results of simulation may be used to better understand the nonlinear beam structure for tissue harmonic imaging in modern medical diagnostic scanners. [Work supported by CRDF and RFBR.]

Fluid property evaluation by using transversal effects of piezoelectric transducer

In this paper, we describe a highly sensitive device that utilizes the transversal effect of rectangular piezoelectric transducer to measure the viscosity of water-based and ionic MFs. This device could monitor the differences in MF types and also have overcome the design limitations of the conventional viscometer for measurements in external magnetic fields.

The directivity pattern of an interferometer for measuring thermal acoustic radiation

The directivity patterns of a pair of piezoelectric transducers for measuring the spatial correlation function of sound pressures produced by sources of thermal acoustic radiation in the megahertz frequency range are calculated. Sources in the form of a heated plane or strip are considered. The signal detection by two circular or rectangular piezoelectric transducers and by focusing transducers is studied. It is demonstrated that, for measuring the correlation function, the piezoelectric transducers must partially overlap. To determine the directivity pattern with a strong dependence on the distance between the heated object and the pair of piezoelectric transducers, focusing piezoelectric transducers should be used. The results obtained offer possibilities for a noninvasive measurement of the absorption coefficient of a medium and also for the realization of the previously proposed [20] passive acoustic thermotomograph, which does not use a priori information on the absorption coefficient of the medium.