Extensional Vibration Mode Research Articles

A Study on the Rectangular-Bar-Shaped Multilayer Piezoelectric Transformer Using Length Extensional Vibration Mode

The rectangular-bar-shaped multilayer piezoelectric transformer, which employs the length extensional vibration mode and interdigital internal electrodes, has been suggested and developed by us for the application to AC adapters. First, the methods of increasing the power-to-volume ratio of the transformer are investigated experimentally. As a result, it is found that using a high driving frequency and optimizing the positions of input and output parts increase the power-to-volume ratio. Second, to prevent characteristic degradation resulting from spurious vibrations in its driving frequency range, the methods of controlling such spurious vibrations are studied theoretically and experimentally. It is found that controlling the size of the transformer can widen the driving frequency range without spurious vibrations, and that using a low order length extensional vibration mode can decrease the number of spurious vibrations in its driving frequency range. Also, it is found that spurious vibrations can be eliminated or weakened by properly arranging the positions of input and output parts according to the mode pattern of the spurious vibrations.

Analysis of Nonlinear Phenomena in Piezoelectric Ceramics under High-Power Vibration

Generation of higher harmonic voltages in piezoelectric ceramics driven at high-power resonance frequency levels was investigated. Rectangular bar samples with a high mechanical quality factor were prepared for this study. The samples were driven at a fundamental resonance frequency of the length extensional vibration mode by a constant current method, and their current, voltage and displacement were simultaneously measured. When the samples were driven at a constant current higher than the threshold level, distinct distortion in voltage waveform was observed while current waveform and displacement were exactly sinusoidal. By analyzing the distorted voltage waves with a spectrum analyzer, the distortion of the voltage wave was found to be due to the generation of higher harmonic voltages. The 2nd and 3rd harmonic voltages were measured as a function of current, and their magnitudes satisfied the power laws of square and cubic of the current, respectively. These experimental results can be explained by nonlinear piezoelectric equations derived from the ferroelectric theory.

An alternative method for the measurement of the clamped capacitance of disk shaped piezoelectric ceramics

Abstract Several measurement methods for the dielectric permittivity at constant strain ε33 S of a piezoelectric ceramic have been proposed1−2. In this paper a comparison of these methods is made and an alternative and complementary method is proposed. This method requires a clear and well shaped thickness resonance and is based on the measurement of the electrical input impedance at the frequencies fs and fp of the fundamental resonance of the thickness extensional mode of vibration. Other parameters - kt and Qm - can also be obtained from these measurements1−3. Several samples of different piezoelectric ceramics have been measured and the results using the proposed and the above mentioned methods are compared.

Rotary Ultrasonic Motor using Extensional Vibration of a Ring

Using the extensional vibration mode of a PZT ring, an ultrasonic rotary motor is successfully made. The PZT ring is radially polarized and acts as a stator of a motor. The traveling wave along the circumference of the ring is obtained by driving two standing waves which are temporally and spatially phase shifted by 90 degrees from each other. A structure similar to a drum brake is employed as a rotor. The maximum torque and maximum efficiency of the motor are 200 g·cm and 1.9%, respectively.

High-frequency core-loss characteristics of biased Fe<inf>79</inf>B<inf>16</inf>Si<inf>5</inf>amorphous metallic-alloy tape-wound cores

The core-loss characteristics of biased magneto-elastically resonant tape-wound cores manufactured from METGLAS® alloy 2605S-3 (composition Fe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">79</inf> B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">16</inf> Si <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</inf> ) are presented. These characteristics are measured under small-signal excitation (constant ΔB) over the frequency range from 10 kHz to 500 kHz using cores of three different sizes. Measurements of the impedance of the cores with windings are used to obtain the incremental relative permeability μ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> over the same frequency range. Both core-loss data and permeability data indicate strong magnetomechanical coupling, with the measured core loss being about 100 times greater at resonance than normal losses due to hysteresis and eddy currents. The dominant mode of mechanical resonance is experimentally confirmed to be due to the fundamental extensional mode of vibration. Young's modulus E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</inf> for constant ΔB is calculated at different dc-bias levels from the resonant frequencies obtained using incremental relative permeability data, and is plotted as a function of bias level for the three core sizes.

Spectral analysis of coal-mine roof vibrations

A study was made of the possibility of assessing coal-mine roof integrity by using audio-frequency-range spectral analysis of the vibrations produced by tapping the roof. Laboratory tests of rock slabs and field tests of mine-roof slabs showed that characteristic bending, torsional, and extensional vibration modes are excited and easily measured. Modes characteristic of a wave bouncing between the face and back of a slab spread and dissipate too rapidly to allow spectral analysis; thus, slab thickness is not measurable by this technique. Solid roofs give broadband, noise-like spectra with little low-frequency energy. “Drummy” roofs give line spectra characteristic of slab vibration modes and usually have considerable energy in the 0–400 Hz range. Spectral analysis can indicate “drummy” versus “nondrummy” but can reveal little about thickness or mounting of a roof slab and can contribute little to practical mine safety. Recommendations are made for better use of normal hearing in mine-roof testing, better protection for those doing the testing, safer mining methods, and for studies of microseismic emissions coming immediately after coal cutting.

Sudden stretching of a four-layered composite plate

A research effort primarily concerned with the understanding of laminated composite plates with cracks subjected to time-dependent extensional loads is reported here. When loads are applied suddenly to a laminate, waves are reflected and refracted through the laminae and give rise to stresses and strains throughout the composite system. The process is three-dimensional in character and presents a formidable problem in the theory of elastodynamics, particularly in the presence of crack-like imperfections. An approximate theory of laminated plates is developed by assuming that the extensional and thickness mode of vibration are coupled. The mixed boundary value crack problem of a four-layered composite plate is solved. Dynamic stress intensity factors for a crack subjected to suddenly applied stress are found to vary as a function of time and depend on the material properties of the laminate. Stress intensification in the region near the crack front can be reduced by having the shear modulus of the inner layers to be larger than that of the outer layers.

Electric field dependence of a contour mode resonance in pzt ferroelectric ceramics

The electric field dependence of resonance frequency of a contour extensional mode of vibration in PZT ferroelectric ceramics was investigated. The bias characteristics of the resonance frequency showed a non-linear behaviour. A discussion of the results is given in terms of 90° domain rotations.The results indicate that rotation of 90° domains play an important role in the electric field dependence of physical constants in this material.

Holographic observation of the parametrically excited vibrational mode of an X-cut quartz plate

The vibrational mode of the flexural vibration excited parametrically by the extensional mode of vibration has been observed by means of the holographic technique. It is shown that the amplitude distribution of the vibration displacement of the parametrically excited mode is identical with that of the directly excited mode.

Effects of Pressure and Fluid Saturation on the Attenuation of Elastic Waves in Sands

Abstract The velocity and attenuation of elastic waves in sandstones were measured as a function of both pressure and fluid saturation. A large change occurs in these quantities if water is added and the rock is not compressed, but the change is small if the rock is subjected to a large overburden pressure. Measurements were made by vibrating cylindrical samples in both the extensional and torsional modes at frequencies up to 30,000 cycles/sec. Formulas were derived which enable the attenuation of dilatational waves in dry rocks to be deduced from the data. Similar experimental methods were used to investigate the properties of unconsolidated sands. Velocities were found to vary with the 1/4 power of the overburden pressure and attenuations to decrease with the 1/6 power. The effects of grain size, amplitude and fluid saturation were studied. Formulas by which the effects produced by a jacket around the sample may be calculated were derived. The practical application of these results to formation evaluation is discussed. Introduction The attenuation of elastic waves in the earth has been of interest to the seismologist and geophysicist for many years, but only recently to the petroleum engineer. Engineering interest has been brought about by the success of velocity logging devices, for it is possible by modification of these instruments to measure the attenuation of sound waves in addition to their velocity and, hence, deduce the mobility of formation fluids as well as the porosities of the rocks which contain them. The main problem is to decide whether field measurements can be made with sufficient accuracy to be of practical use. This problem can only be solved after we know the magnitude of the attenuations which are typical of the earth at various depths. The logarithmic decrement of a fluid-saturated rock is the sum of a "sloshing" decrement and a "jostling" decrement, the former caused by the mobility of the fluid contained within the rock and the latter by the granular framework of the rock. Sloshing decrements can be calculated using Biot's theory, but the jostling losses are less well understood. The present paper reports an experimental investigation of jostling losses in consolidated and unconsolidated sands, particularly with respect to the effect of overburden pressure and fluid saturation. Born showed that the decrement of a sandstone may increase dramatically when only a few per cent by weight of distilled water is added, and that the additional loss is proportional to the frequency of vibration. His measurements were made with no compressive stress on the framework of the rock. M. Gondouin investigated similar phenomena for fluid-saturated plasters but also did not compress the samples. In the present paper it is shown that compression of the framework reduces this effect, so that at depth the jostling decrement of a sandstone may be expected to be almost independent of fluid saturation and frequency. Decrements for many sedimentary rocks have been given by Volarovich, but all for the state of zero overburden pressure. Anomalously low velocities have been logged in shallow unconsolidated gas sands. Results of the present investigation confirm that these velocities are not caused by correspondingly high attenuations, because the jostling decrement in a packing of sand grains is small and much less than in a consolidated sandstone at the same depth. Velocities in sands have been measured by Tsareva and by Hardin as a function of pressure, but the corresponding decrements do not appear to have been measured previously. The widely used "resonant bar method" of measuring velocities and decrements was employed. Comments on variations of this technique have recently been published by McSkimmin. The main novelty of the present technique was the application of pressure to the samples. It was found possible to do this by placing the apparatus inside a pressure vessel, provided the conditions leading to large additional losses were avoided. These conditions are discussed below. EXPERIMENTAL TECHNIQUE Cylindrical samples were caused to vibrate in both the extensional and torsional mode of vibration and the amplitude of vibration was measured as a function of frequency in the neighborhood of a resonant frequency. The resonant frequency, fr, is related to the corresponding elastic modulus by the formulas where E and N are Young's modulus and the modulus of rigidity, p is the density of the sample, and the wavelength of the vibration. JPT P. 189ˆ

Loading of quartz oscillator plates

The effects of physically loading the surface of two types of piezoelectric quartz oscillator plates have been experimentally investigated. Various amounts of Wood's metal were applied to different parts of the crystal surfaces. Thickness-shear-mode plates were benefited only when the metal was applied on or near the active central area of the plate, but X-cut crystals employing an extensional mode of vibration responded favorably only when the metal was applied near the periphery of the plate. In both types of oscillator plates loading increased the crystal unit Q several fold. Activity-frequency characteristics over a temperature range —60° to +90°C were greatly improved.