Showing papers in "IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control in 1989"
TL;DR: In this paper, a theoretical model is presented for combining parameters of 1-3 ultrasonic composite materials in order to predict ultrasonic characteristics such as velocity, acoustic impedance, electromechanical coupling factor, and piezoelectric coefficients.
Abstract: A theoretical model is presented for combining parameters of 1-3 ultrasonic composite materials in order to predict ultrasonic characteristics such as velocity, acoustic impedance, electromechanical coupling factor, and piezoelectric coefficients. Hence, the model allows the estimation of resonance frequencies of 1-3 composite transducers. This model has been extended to cover more material parameters, and they are compared to experimental results up to PZT volume fraction nu of 0.8. The model covers calculation of piezoelectric charge constants d/sub 33/ and d/sub 31/. Values are found to be in good agreement with experimental results obtained for PZT 7A/Araldite D 1-3 composites. The acoustic velocity, acoustic impedance, and electromechanical coupling factor are predicted and found to be close to the values determined experimentally. >
355Â citations
TL;DR: A method for computing array element amplitude and phase distributions for direct synthesis of multiple-focus field patterns using ultrasonic phased arrays is shown to be capable of producing desired field levels at a set of control points in the treatment volume, providing a powerful tool for hyperthermia treatment planning.
Abstract: A method for computing array element amplitude and phase distributions for direct synthesis of multiple-focus field patterns using ultrasonic phased arrays is shown to be capable of producing desired field levels at a set of control points in the treatment volume. The complex pressure at any of these control points can be chosen to produce the desired power deposition at the point, including reducing the field level to avoid potential hot spots, thus providing a powerful tool for hyperthermia treatment planning. The method also allows the complex excitation vector to be weighted to reduce the dynamic range of the driving signals without disturbing the relative field levels at the control points, allowing near maximum power transfer from the array into the treatment volume. >
293Â citations
IBM1
TL;DR: A method is presented for calculation of the sound field from a rectangular continuous-wave source surrounded by a plane grid baffle, which shows that the transverse pressure distribution is more uniform in the near-field of the square source.
Abstract: A method is presented for calculation of the sound field from a rectangular continuous-wave source surrounded by a plane grid baffle. The approach is illustrated for square sources of 0.5, 1, 2, 5, 10, 20, and 100 lambda on a side. These results are compared to the sound fields produced by similarly sized circular sources. The beam widths and locations of on-axis minima are similar for the two sources, but the transverse pressure distribution is more uniform in the near-field of the square source. The effects of attenuation on the sound field of a square source are examined. >
190Â citations
TL;DR: An approximate analytical formulation is presented that allows for the calculation of acoustic pressure thresholds for transient cavitation over a variety of frequencies and host fluid parameters.
Abstract: An approximate analytical formulation is presented that allows for the calculation of acoustic pressure thresholds for transient cavitation over a variety of frequencies and host fluid parameters. Specifically, R.E. Apfel's (1986) theory is extended to include an estimate of the time delay associated with the Laplace pressure, 2 sigma /R/sub 0/, where sigma is the surface tension and R/sub 0/ is the initial radius. Also presented is a correction factor for the time-averaged pressure difference, across the bubble wall during growth. An optimum size distribution of nuclei for the predisposition of a sample to microcavitation is exhibited. The role of transient cavitation in medical ultrasound is discussed. >
187Â citations
TL;DR: An ultrasonic motor using bending vibrations of a short cylinder with free-free ends is proposed, and its performance and efficiency are discussed.
Abstract: An ultrasonic motor using bending vibrations of a short cylinder with free-free ends is proposed, and its performance and efficiency are discussed. The motor is small in size and realizes a high mechanical output of more than 1 W. The general principle of the motor, which uses traveling waves, is as follows. When a traveling wave propagates along an elastic object, particles at the surface move elliptically. A movable object (a slider or a rotor) pressed to the elastic object may be caused to move due to the frictional forces between it and the surface. A motor based on this principal has been constructed and studied. The vibration mode used is found to have an undesirable radial component, which restricts the efficiency of the motor to about 10% at best. A large amount of the energy supplied is lost by the slippage owing to the existence of the undesirable component. It is concluded that to derive larger output power, the frictional material needs to be carefully chosen. >
130Â citations
NEC1
TL;DR: An electric ultrasonic transducer is developed by using a silicon IC process to obtain high sensitivity and the desired frequency responses in air, and should be helpful in the design of phased-array transducers integrated with electronic scanning circuits.
Abstract: An electric ultrasonic transducer is developed by using a silicon IC process. Design considerations are first presented to obtain high sensitivity and the desired frequency responses in air. The measured transmitter sensitivity is 19.1 dB (0 dB=1 mu bar/V) at a point 50 cm away from the devices, when the devices are operated at 150 kHz. The receiving sensitivity is 0.47 mV/Pa in the 10-130-kHz range, with bias voltages as low as 30 V. An electronic sector scanning operation is also achieved by time-sequentially driving seven elements arranged in a linear array on the same chip. The results should be helpful in the design of phased-array transducers integrated with electronic scanning circuits. >
109Â citations
TL;DR: Comparisons between the models and actual film transducers show excellent broadband simulation of both electrical input impedance and ultrasonic pulse-echo performance.
Abstract: A method is presented for determining the piezoelectric constants and the frequency-dependent dielectric properties of the polymers from a five-step algorithm based on analysis of air-loaded broadband impedance measurements. It is shown how to account for the frequency-dependent lossy properties of these films in an equivalent impedance circuit model and a modified Mason's model. Comparisons between the models and actual film transducers show excellent broadband simulation of both electrical input impedance and ultrasonic pulse-echo performance. >
96Â citations
TL;DR: In this paper, the dielectric constant and spontaneous polarization of fine-grained BaTiO/sub 3/ prepared from powder produced by metalloorganic decomposition technology were studied.
Abstract: The dielectric constant and spontaneous polarization of fine-grained BaTiO/sub 3/ prepared from powder produced by metalloorganic decomposition technology were studied The room-temperature dielectric constant of BaTiO/sub 3/ was found to increase sharply with increase in grain size, reach a maximum at about 04 mu m, and decrease with further increase in grain size Spontaneous polarization continuously decreased with decrease in grain size A model is proposed to explain the grain size dependence of the dielectric constant >
94Â citations
TL;DR: A model for the grain signal is presented, which includes the effect of frequency-dependent scattering and attenuation, and it is shown that the expected frequency shift can be correlated with the grain size of the material.
Abstract: A model for the grain signal is presented, which includes the effect of frequency-dependent scattering and attenuation. This model predicts that the expected frequency increases with scattering and decreases with attenuation. Homomorphic processing was used for spectral smoothing, and the selection of parameters for optimal performance was examined. Experimental results are presented that show both the upward shift in the expected frequency with grain boundary scattering and the downward shift with attenuation. Furthermore, it is shown that the expected frequency shift can be correlated with the grain size of the material. It is important to point out that the quantitative relationship between the average grain size and the expected frequency shift (either upward or downward) is dependent on the type of material, the quality of grain boundaries, and the characteristics of the measuring instruments. >
87Â citations
TL;DR: Using a dual track sector-vortex array with practical ranges of the aperture size and number of elements, acoustic power deposition patterns capable of heating the peripheral and central regions of a nonsuperficial tumor a few centimeters in diameter are obtained by computer simulation.
Abstract: A sector-vortex phased array capable of generating directly annular-shape foci is analyzed. By driving the sectors of the array with signals whose phase rotates M times around the circular track, annular foci with the same acoustic-signal-phase rotation are produced in the geometrical focal plane of the array. Because of this phase modulation around the focal annuli and the resulting high-spatial-frequency content, the produced acoustic fields are free from secondary foci both behind and in front of the focal plane. The diameter of the focal annuli can be increased by increasing the mode number M. By providing the array with multiple tracks, it is possible to get larger focal annuli than with a single track with the same mode number M. It is also possible to achieve some control of the power deposition patterns in the depth direction in this way. Using a dual track sector-vortex array with practical ranges of the aperture size and number of elements, acoustic power deposition patterns capable of heating the peripheral and central regions of a nonsuperficial tumor a few centimeters in diameter are obtained by computer simulation. >
85Â citations
TL;DR: The mass loading effects of adsorbing and desorbing contaminant molecules on the magnitude and characteristics of frequency fluctuations in a thickness-shear resonator are studied in this paper.
Abstract: The mass loading effects of adsorbing and desorbing contaminant molecules on the magnitude and characteristics of frequency fluctuations in a thickness-shear resonator are studied. The study is motivated by the observation that the frequency of a thickness-shear resonator is determined predominantly by such mechanical parameters as the thickness of the resonator, elastic stiffnesses, mass loading of the electrodes, and energy trapping. An equation was derived relating the spectral density of frequency fluctuations to: (1) rates of adsorption and desorption of one species of contaminant molecules; (2) mass per unit area of a monolayer of molecules: (3) frequency constant; (4) thickness of resonator; and (5) number of molecular sites on one resonator surface. The induced phase noises were found to be significant in very-high-frequency resonators and are not simple functions of the percentage of area contaminated. The spectral density of frequency fluctuations was inversely proportional to the fourth power of the thickness if other parameters were held constant. >
TL;DR: A phased-array field conjugation method is investigated as a means for synthesizing directly many ultrasound field patterns useful for tumor heating, which offers the possibility of creating simultaneously, at different sites, more than one focus, which can be scanned electronically.
Abstract: A phased-array field conjugation method is investigated as a means for synthesizing directly many ultrasound field patterns useful for tumor heating. For virtually any ultrasound phased array, the method permits the computation of element driving amplitude and phase distributions appropriate for synthesizing directly diffuse heating patterns without the need for mechanical or electrical scanning. Moreover, the proposed method offers the possibility of creating simultaneously, at different sites, more than one focus, which can then be scanned electronically. This attractive feature eliminates the need for operating at high spatial-peak temporal-peak focal intensities, a potential problem associated with conventional scanning, while achieving a desired heating pattern. The method is applied to two different applicator configurations: a concentric-ring and a square n*n array. Computer simulations of different heating patterns, synthesized using the field conjugation method, are presented. Important practical design parameters, such as the size and number of the array elements, are discussed. >
TL;DR: In this paper, crack-free and dense BaTiO/sub 3/ films 4 to 8 mu m thick were prepared by spinning a solution of metalloorganic precursors onto an appropriate substrate, and firing and annealing the film in air at certain temperatures to obtain appropriate grain sizes.
Abstract: Crack-free and dense BaTiO/sub 3/ films 4 to 8 mu m thick were prepared by spinning a solution of metalloorganic precursors onto an appropriate substrate, and firing and annealing the film in air at certain temperatures to obtain appropriate grain sizes. The electrical properties of the films were studied as a function of grain size, temperature, frequency, and DC bias. Films with a grain size of 0.2 mu m showed ferroelectric properties similar to bulk BaTiO/sub 3/. >
TL;DR: The integrated backscatter calculation over the full, two-dimensional echocardiographic sector is implemented to produce images from closed-chest dogs and allows a continuous determination of integrated back scatter from all myocardial regions in the ultrasonic view.
Abstract: The integrated backscatter calculation over the full, two-dimensional echocardiographic sector is implemented to produce images from closed-chest dogs. This new real-time integrated backscatter measurement system allows a continuous determination of integrated backscatter from all myocardial regions in the ultrasonic view. By replacing the conventional video processor in a commercial two-dimensional echocardiographic imager with this new real-time backscatter measurement system, it is possible to produce real-time two-dimensional images based on integrated backscatter. >
TL;DR: The results for this particular gripper indicate that the additional sensory feedback can decrease the force step response rise time by 88% while maintaining a monotonic zero-overshoot response.
Abstract: A novel robot gripper control system is presented that uses PVDF (polyvinylidene fluoride) piezoelectric sensors to damp exerted force actively. By monitoring the current developed by the PVDF sensor, an output proportional to the rate of change of the force exerted by the gripper is obtained. The signals from the PVDF sensor and strain-gauge force sensor are arranged in a proportional and derivative control system for the control of force. The control system was tested on an instrumented Rhino XR-1 manipulator hand. The capabilities of the control system are analyzed and are verified experimentally. The results for this particular gripper indicate that the additional sensory feedback can decrease the force step response rise time by 88% while maintaining a monotonic zero-overshoot response. The inclusion of the rate feedback increases the damping ratio of the dominant poles while maintaining the step response rise time. >
TL;DR: A polarity thresholding algorithm that has recently been developed for split-spectrum processing for ultrasonic coherent noise reduction is theoretically analyzed to evaluate its performance and some experimental results of SNR enhancement obtained with this algorithm are presented.
Abstract: A polarity thresholding algorithm that has recently been developed for split-spectrum processing for ultrasonic coherent noise reduction is theoretically analyzed to evaluate its performance. The probability density function (PDF) of the output of the algorithm is derived and used to calculate the theoretical signal-to-noise ratio (SNR) enhancement and the receiver operating characteristics. The performance limits of the algorithm are also established. Some experimental results of SNR enhancement obtained with the polarity thresholding algorithm are presented. >
TL;DR: A transit-time ultrasonic gas flowmeter for high-rangeability requirements, such as those encountered in flare-gas flow-metering, is presented and the concept of ray rescue angle for the orientation of the ultrasonic transducers in single-beam transit- time ultrasonic flowmeters is introduced.
Abstract: A transit-time ultrasonic gas flowmeter for high-rangeability requirements, such as those encountered in flare-gas flow-metering, is presented. The concept of ray rescue angle for the orientation of the ultrasonic transducers in single-beam transit-time ultrasonic flowmeters is introduced to overcome the problem of ultrasonic beam drift in high-velocity flows. To overcome problems associated with noise at high velocities, a chirp signal is used. To preserve the accuracy of the meter at low velocities near zero flow, a combination of chirp and continuous-wave signals is used to interrogate the flow. Overall system performance is presented, based on results from extensive wind-tunnel tests. >
TL;DR: Pure (undoped) piezoelectric lead zirconate titanate (PZT) ceramic samples at compositions across the ferroelectric region of the phase diagram were prepared from sol-gel-derived fine powders to obtain dense ceramics with large grain size and to control the lead stoichiometry.
Abstract: Pure (undoped) piezoelectric lead zirconate titanate (PZT) ceramic samples at compositions across the ferroelectric region of the phase diagram were prepared from sol-gel-derived fine powders. Excess lead oxide was included in the PZT powders to obtain dense (95-96% of theoretical density) ceramics with large grain size (>7 mu m) and to control the lead stoichiometry. The dielectric, piezoelectric, and elastic properties were measured from 4.2 to 300 K. At very low temperatures, the extrinsic domain wall and thermal defect motions freeze out. The low-temperature dielectric data can be used to determine coefficients in a phenomenological theory. The extrinsic contribution to the properties can then be separated from the single-domain properties derived from the theory. >
TL;DR: In this article, experimental and theoretical investigations of the electromechanical anisotropy of ceramics modified with Ca, Ni-Nb, and Mn are presented, and it is demonstrated that the large anisotropic properties of these materials are neither a bulk property of the PbTiO/sub 3/-crystallites nor a domain wall effect.
Abstract: Experimental and theoretical investigations of the electromechanical anisotropy of ceramics modified with Ca, Ni-Nb, and Mn are presented. It is demonstrated that the large anisotropy of these ceramics is neither a bulk property of the PbTiO/sub 3/-crystallites nor a domain wall effect. The anisotropy is caused by the statistical orientation of the crystallites in the ceramics and by the material properties due to this orientation. The ratio of electrostrictive coefficients and the ratio of single-crystal permittivities in these ceramics also play a decisive role. The result enables one to comprehend easily the dependence of the ceramic's electromechanical anisotropy on the material composition, the degree of poling, and the temperature. >
TL;DR: A newly developed motor concept which allows a bidirectional piezoelectric ultrasonic motor to be operated with only a single voltage feed and thus only one power amplifier is described.
Abstract: The authors describe a newly developed motor concept which allows a bidirectional piezoelectric ultrasonic motor to be operated with only a single voltage feed and thus only one power amplifier. The motor concept is based on the superposition of a longitudinal and a flexural oscillation of a rod-shaped resonator. In a way analogous to the generation of a Lissajous figure, this superposition produces a rotary movement of the resonator end by means of which a rotor is directly driven. By selecting the relative phase of the electrical stimulations of both modes, the speed can be continuously varied in both directions. The motor can be driven in both right and left directions with speeds of 0 to 300 r/min, and a freewheeling state can be set up by means of a suitable phase between the oscillation modes. In the off state, the motor blocks the motion. >
TL;DR: The use of grain-oriented Bi/sub 4/Ti/sub 3/O/sub 12/ ceramics as a high-temperature piezoelectric transducer is suggested.
Abstract: The concept of grain-oriented fabrication in ceramics, which utilizes anisotropy either in morphology or some specific property of the particle, is reviewed. A fabrication method, which maximizes the grain orientation, is described for Bi/sub 4/Ti/sub 3/O/sub 12/. The process utilized plate-like morphology of Bi/sub 4/Ti/sub 3/O/sub 12/ particles and yielded a ceramic with an X-ray density of 95.4% and an unprecedented value of 100% for Lotgering's orientation factor in the direction of orientation. The dielectric and piezoelectric properties of this ceramic are described and compared to single crystal values. Complex impedance analysis of the ceramics was used to explain the dielectric relaxations at elevated temperatures. The use of grain-oriented fabrication as a practical technique for making polycrystalline ceramics with electrical properties close to those of single crystals (in the direction of orientation) is emphasized. The use of grain-oriented Bi/sub 4/Ti/sub 3/O/sub 12/ ceramics as a high-temperature piezoelectric transducer is suggested. >
TL;DR: The calculated velocity dispersion and electromechanical coupling factors for plate modes in representative piezoelectric materials are described and frequency dependence of velocity and electromechanical coupling factors are given.
Abstract: Recent theoretical studies and experiments have been shown that interdigital transducers can couple strongly to plate modes in piezoelectric materials and in piezoelectric-on-nonpiezoelectric composite membranes. The calculated velocity dispersion and electromechanical coupling factors for plate modes in representative piezoelectric materials are described. The frequency dependence of velocity and electromechanical coupling factors are given, under different metallization conditions, for generalized stiffened-Lamb, pure stiffened-Lamb, and stiffened-shear (shear-horizontal) modes, for various plate orientations in lithium niobate, lithium tantalate, quartz, bismuth germanium oxide, and zinc oxide. For lithium niobate, electromechanical-coupling values as high as 15% are found under narrowband bandpass conditions, and 5% under wideband low-pass conditions. For lithium tantalate, bismuth germanium oxide, coupling values of 0.5, 2, and 4% are obtained. For quartz with its weaker piezoelectricity, the coupling is still made smaller. >
TL;DR: A method of image restoration for ultrasonic B-scan images has been proposed that need no a priori knowledge on the PSF (point spread function) of the imaging system and is feasible for in vivo applications.
Abstract: A method of image restoration for ultrasonic B-scan images has been proposed that need no a priori knowledge on the PSF (point spread function) of the imaging system and is feasible for in vivo applications. The entire system's response, including the interposed medium and possible transducer defects, is estimated from the degraded image itself with a few simple operations. The ultrasonic image is restored based only on a knowledge of the estimated PSF and on the spectral characteristics of the resultant echo signal. The proposed method does not modify the phase relations between echoes from multiple scatterers since the restoration filter is phaseless and the display operation does not involve nonlinear detection. The effectiveness of the restoration filter was tested on simulated ultrasonic images in the absence and in the presence of interposed tissue. Then the filter was tested on a phantom made of scatterers randomly distributed in nonattenuating gel with and without an interposed medium whose attenuation linearly increases with frequency. A good correspondence between simulations and experimental results was found: both tests show an exceptional improvement of image resolution. >
TL;DR: In this paper, a computer simulation model of the nonstationary Doppler ultrasound signals arising from pulsatile blood flow is presented, which uses sinusoidal components that are modulated by a power spectral density function that varies over the cardiac cycle.
Abstract: A computer simulation model of the nonstationary Doppler ultrasound signals arising from pulsatile blood flow is presented. The model uses sinusoidal components that are modulated by a power spectral density function that varies over the cardiac cycle. An empirical model consisting of two exponential functions is used to represent both the continuous wave and pulsed Doppler power spectral density for normal carotid arteries. It is shown that the spectrogram speckle patterns of the synthesized Doppler signals compare very well with those clinically recorded. >
TL;DR: Experimental results support the conclusion that scatterer size is a feasible tissue characterization parameter and the reliability of the estimation of the size of scattering structures is assessed.
Abstract: The reliability of the estimation of the size of scattering structures is assessed by realistic simulations and phantom experiments. The acoustic tissue model used in the simulation studies comprised a constant sound speed, homogeneous attenuation, and isotropic scattering. The scattering models considered were a discrete (spherical) model and two inhomogeneous-continuum models. The latter were characterized by an exponential and a Gaussian autocorrelation function, respectively. The backscattering spectra were, over the range from 5 to 10 MHz, fitted to linear, power, and autocorrelation functions of the three scattering models. The effects of the fitting function, the attenuation-either in an intervening layer or within the region of interest (ROI)-of the transmission pulse, and a spread in the scatterer sizes on the accuracy and the precision of the size estimates were assessed. The attenuation in the intervening tissue layer(s) as well as in the ROI itself has a significant effect on the accuracy of the size estimates and needs to be corrected. When performing the attenuation correction the inaccuracy of the attenuation estimate of the intervening layer leads to a large bias in the estimated scatterer size. Experimental results support the conclusion that scatterer size is a feasible tissue characterization parameter. >
TL;DR: The results show that the best tested predictor of bubble response is the pressure amplitude of the fundamental frequency in a Fourier series expansion of the distorted pulse, and theoretical thresholds for transient cavitation induced by a distorted pulse are presented.
Abstract: Prediction of the response of gas-filled microbubbles to ultrasound waves is complicated by the finite-amplitude distortion associated with large-amplitude acoustic fields. Typical finite-amplitude pulses in medical applications consist of a sharp positive spike followed by a smaller slowly varying negative pressure. A suitable model for pressure waveforms that have these temporal characteristics is described, and the response of microbubbles to such sound fields is subsequently computed. A selection of descriptive parameters is considered to determine the characteristic features of the distorted pulse which are most important in generating bubble response. The results show that (a) the peak-positive pressure is a very poor predictor of bubble response; (b) the peak-negative pressure typically underestimates the bubble response; and (c) the best tested predictor of bubble response is the pressure amplitude of the fundamental frequency in a Fourier series expansion of the distorted pulse. Theoretical thresholds for transient cavitation induced by a distorted pulse are presented for a range of frequencies and initial sizes of microbubbles. >
TL;DR: The concept of a caustic is shown to be an excellent way of characterizing SAW focusing by a circular-arc interdigital transducer on YZ-LiNbO/sub 3/.
Abstract: Using the angular spectrum theory and experimental velocity data of surface acoustic waves (SAW) on YZ-LiNbO/sub 3/, the focusing characteristics of a circular-arc interdigital transducer have been demonstrated. The calculated results show that the depth of focus is long and the compressed acoustic beam width is very narrow. The concept of a caustic is shown to be an excellent way of characterizing SAW focusing by a circular-arc interdigital transducer on YZ-LiNbO/sub 3/. Comparison between theoretical and experimental results shows good agreement. >
TL;DR: It is shown that real-time reconstruction is feasible using the concepts of parallel processing and that a special multisegment sensor results in a significant improvement in signal-to-noise ratio and image quality and that the reconstructed image benefits from the concurrent activation of multiple receivers per transmitted pulse.
Abstract: An evaluation of the application of a parallel-processing array to the measurement of two-phase flow, such as bubbly oil flow through a pipe, in real-time is described. Pulse-echo ultrasound tomography is used to generate a cross-sectional image of the flow that forms the basis for the deduction of flow parameters, such as the void fraction. The tomographic algorithm used is backprojection adapted for execution on an array of parallel-processing devices. It is shown that real-time reconstruction is feasible using the concepts of parallel processing. Different sensor arrangements were investigated by computer simulation. It is shown that a special multisegment sensor results in a significant improvement in signal-to-noise ratio and image quality and that the reconstructed image benefits from the concurrent activation of multiple receivers per transmitted pulse. The findings may also be useful for nondestructive testing and medical applications. >
TL;DR: The validity of the predictions derived from the one-dimensional analytical theory for longitudinal ultrasonic resonators was tested with respect to this application by means of finite-element calculations and showed that maximum final amplitude is attained when the resonator tapers as steeply as possible.
Abstract: An ultrasonic piezoelectric motor concept is presented that is based on the transformation of the longitudinal oscillations of a rod-shaped resonator into continuous motion by arranging the resonator diagonally to a drum. The efficiency of the motor was enhanced by increasing the amplitude of motion at the point of motion transfer by tapering the resonator. To optimize the resonator design, the validity of the predictions derived from the one-dimensional analytical theory for longitudinal ultrasonic resonators was tested with respect to this application by means of finite-element calculations. The one-dimensional calculation turned out to be hardly applicable at all to real resonators. The finite-element calculations showed that maximum final amplitude is attained when the resonator tapers as steeply as possible, no preference being shown for any special mathematical form of cross-sectional reduction. Efficiencies of 35% and torques of 25 N-cm were attained at 150 r/min. >
TL;DR: A model relating the velocity shifts of surface acoustic waves (SAW) to the six tensor components of quasistatic stresses makes it possible to define a family of quartz cuts with potentially low stress and temperature sensitivities for oscillator applications.
Abstract: A model is presented, relating the velocity shifts of surface acoustic waves (SAW) to the six tensor components of quasistatic stresses. Stress sensitivity is then defined through six independent coefficients, whatever the origin of the stress (direct external forces, thermoelastic stresses) might be. These coefficients, depending on crystal anisotropy, are computed for different cut angles and propagation directions of quartz crystal, and represented as a contour-line mapping. The determination of SAW quartz cuts compensated for both planar isotropic stresses and first-order temperature effects make it possible to define a family of quartz cuts with potentially low stress and temperature sensitivities for oscillator applications. >