Collinear Array Research Articles

The linear steady thermoelastic problem for a strip with a collinear array of Griffith cracks parallel to its edges

The problem of determining the thermal stresses when a uniform heat flow in a thermoelastic strip is disturbed by a collinear array of cracks is discussed. The solution of the Duhamel-Neumann equations is posed in terms of harmonic functions, which leads to dual series relations whose solutions are known. Numerical results for the stress intensity factors at the crack tips are displayed in graphical form.

Elastic-plastic analysis of a collinear array of cracks on a bimaterial interface

Abstract In previous studies, we found that although the near-tip fields of cracks on a bimaterial interface do not have a separable form of the Hutchinson-Rice-Rosengren (HRR) type, they appear to be nearly separable in an annular region well within the plastic zone. Furthermore, the fields bear interesting similarities to mixed mode HRR fields for homogeneous media. Over length scales comparable to the size of the dominant plastic zone, the stress levels in both materials are set by the yield strength of the weaker (lower yield strength) material. Over distances which are small compared with the smallest dimension of the plastic zone (or distances comparable with the crack tip opening displacement), the behavior of the stresses is governed by the strain hardening characteristics of the more compliant (lower hardening) material. Asymptotically, as the crack tip is approached, the material system responds like that of a plastically deforming solid bonded to a rigid substrate; in particular, the stress and the strain fields in the more compliant material behave like those of a material with identical plastic properties bonded to a rigid substrate. Guided by this observation, our attention is directed to the plane strain problem of a deformable material bonded to a rigid substrate. The bimaterial interface is populated by a row of collinear cracks. The body is loaded by remote tension so that the cracks remain effectively open over size scales that are physically relevant. Contained and large-scale yielding solutions for cracks with crack-length-to-ligament ratios that differ by more than two orders of magnitude are obtained by finite element analysis. The solutions reveal that the effects of load (or finite ligament plasticity) and geometry on the near-tip fields are adequately accounted for by the J integral. Furthermore, the near-tip fields appear to possess a structure which is similar to that already presented in previous publications on the small-scale yielding problem. Over the full range of loads considered, the relation between the crack opening displacement (measured at the center of the crack) and the J integral is not sensitive to differences in geometry associated with widely different crack-length-to-ligament ratios.

Transformation zone shape in ceriapartially-stabilized zirconia

Observations of the steady-state transformed zone around a quasistatically grown crack in Ce-TZP are reported for various temperatures between −40 and 100°C. At room temperature, the zone length ahead of the crack is approx 200 μm, which is much larger than the zone height of approx 40 μm. At lower temperatures, shear bands emanating from the crack tip are also observed, which extend to a few millimetres at the lowest temperature investigated (−40°C). A modification of the DBCS model of plastic yielding is presented, using a collinear array of half-lines of strain to represent the roomtemperature transformed zone. It is noted that the shear component of the transformation strain does not affect the toughening due to such collinear zones. Estimates of the critical transformation stress and the volume fraction transformed, derived from the theoretical model, are shown to compare favourably with available experimental data. Some implications of the present observations for the modelling of transformation-induced plasticity in Ce-TZP are briefly discussed.

A New Look at I.P. Electrode Arrays

Over the past several years little attention has been paid to the electrode arrays used in induced polarisation (IP) surveys. However, arrays are very important in relation to anomaly detection and interpretation and to survey cost. Currently popular arrays are gradient and dipole?dipole. Other arrays are used for resistivity surveying, but generally suffer more inductive coupling. Some new arrays have been investigated in order to look at: the advantages of current or potential dipoles parallel to strike; the virtues of broadside arrays; minimisation of inductive coupling; and a possible reduction in survey costs. A perpendicular dipole?dipole array can reduce inductive coupling with horizontal layers and give an IP anomaly similar to that from a collinear array, if run across strike with both dipoles oblique to strike. Rather different, crossover type, responses are obtained with an L-array, in which one dipole is parallel to the strike of a target zone. This arrangement may locate the target more clearly. A broadside parallel dipole?dipole array can take advantage of the common strike elongation of a target deposit, and relative to a collinear array run across strike, can provide improved resolution, dip information, and efficiency in reconnaissance. Some of the features and benefits of various arrays are demonstrated by modelling results. With further work, including development of interpretation methods, attempts can be made to optimize array geometry for a specific exploration scenario.

Effect of directivity on the sound field produced by a source above a reflecting plane

In this paper, the effect of source directivity on the sound field produced by a source near a reflecting plane by using a collinear array of point sources operating in phase, located above a reflecting plane, but in an otherwise reflection-free environment is analytically and experimentally investigated. It was found that the presence of the reflecting plane and the source directivity can have a considerable effect on the sound pressure levels (SPL). When radiating a third-octave band of noise centered at 500 Hz, for example, the variations in SPL with source orientation were as much as 12 dB. Furthermore, the maximum correction factor occurred when the mainlobe of the source directivity pattern pointed toward the reflecting plane rather than, as might be expected, toward the receiver. Finally, reasonably good agreement is found between the measured and corrected SPL, with the rms error being less than 2.6 for the 500-Hz octave and third-octave bands.

Effect of directivity on the sound field produced by a source above a reflecting plane

In describing equipment sound emissions, it is desired to measure its noise radiation spectra with the equipment located in an anechoic or reflection-free environment. In practice, however, there are a number of situations where sound measurements are made with the equipment in hemi-anechoic space, in which case the equipment is located on a reflecting plane, but in an otherwise reflection-free environment. One problem associated with measurements made in hemi-anechoic environments is that the sound spectra measured under these conditions are not necessarily the same as the spectra that would be produced by the source in the absence of the reflecting plane. Investigators have sought to reconstruct the spectra that would be measured in anechoic space from measurements of spectra made with the source in a hemi-anechoic environment by assuming the equipment to be a point source located above a reflecting plane. In this paper, we examine the effect of directivity on measurements made in a hemi-anechoic environment by computing and measuring the sound field produced by a collinear array of five point sources. Our results show that source directivity has a considerable effect on the radiated sound pressure levels. Finally, the maximum sound pressure levels occur when the major lobe in the source directivity is directed toward the reflecting plane.

Bearing Estimation of Signals Received by a Spatially Distributed Array of Sensors Using Maximum Entropy Method for Spectral Analysis

Precise bearing estimation of signals received by a relatively small number of spatially distributed array of sensors can be done by exploiting high resolution property of the maximum entropy spectral analysis (MESA) procedure. It becomes evident from the results obtained in our experiments that fairly accurate estimate of bearing is possible in the case of K, the number of sensors, as small as Ave provided we make use of complex samples. Further, with K=5 and making use of complex samples it is possible to estimate bearing within 5% acuracy of signal which is 10 dB below a strong interference about 20° off from the signal. The accuracy increases with increasing K and also increasing the level of the signal. It thus appears that higher resolution in MESA can be exploited in bearing estimation of signals received by a spatially distributed collinear and equispaced array of sensors.

A wide-band omnidirectional vertical shaped-beam collinear array

The electrical and physical characteristics of a shaped-beam vertical collinear array antenna are described. The array was designed for operation in two principal 20-MHz bands centered at approximately 1227 and 1575 MHz. The patterns are omnidirectional in azimuth and shaped to provide near-constant gain coverage in the elevation sector from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5\deg</tex> to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">30\deg</tex> . Measured voltage standing-wave ratio (VSWR), gain, and pattern characteristics are presented.

Design of collinear longitudinal slot arrays fed by boxed stripline

An analytical design method is presented which enables determination of the length of each slot in a collinear array and the tilt angle of the strip relative to each slot for a specified aperture distribution and input impedance, in the presence of external mutual coupling. The theory uses an extension of Stevenson's approach to relate the TEM mode current in the boxed stripline to the slot-voltage, and a geometrical theory of diffraction (GTD) expression for the external coupling between slot elements. A novel method is introduced to constrain resonant slot lengths to practical values. An array constructed to validate the theory has given good results.

High‐accuracy magnetic field difference measurements and improved noise reduction techniques for use in tectonomagnetic studies

Previous geomagnetic field measurements in Colorado have been extended using three self‐calibrating rubidium magnetometers accurate to about 0.01 γ. The magnetometers were deployed either in an L‐shaped array or in a collinear array and provided simultaneous measurements of the scalar field at sites separated by 12–16 km. Previous noise reduction work using two‐station magnetic field difference data from Colorado removed variations from the east‐west scalar difference which were correlated with variations in the field component D. The earlier analysis work has been extended to remove also noise correlated with the field components H and Z. Noise due to susceptibility and magnetization differences between sites or induced currents in conductivity anomalies is reduced by this technique. However, the main purpose of this paper is to demonstrate a new noise reduction technique that removes noise due to large‐scale gradients in geomagnetic variations. In effect, the method removes variations in the magnetic field difference between two sites which are correlated with variations in the difference between two other sites in a collinear array. This approach, which does not require vector data, reduced gradiometer noise to 0.03 γ rms for 37 days of hourly averages.

Measurement of Mutual Coupling in a Linear Array of Printed Dipoles

Self impedance of a flat printed dipole with the two elements on two opposite sides of a dielectric substrate has been measured experimentally. The element is fed with a parallel stripline and it is observed that incorporation of a quarter wave transformer at the input of the dipole modifies its self impedance. Measurements of mutual coupling between elements of a collinear array of printed dipoles are carried by designing 3-element and 5-element arrays. Variation of coupling with distance between the elements is measured and compared with the approximate theoretical variation.

The trap-loaded cylindrical antenna

The trap-loaded cylindrical antenna is a cylindrical antenna having one or more traps located in its arms. The traps are either parallel inductor-capacitor circuits or short-circuited transmission line stubs that are designed to be antiresonant (having essentially an infinite input impedance) at some particular frequency. The location and the antiresonant frequency of the traps are selected to enhance the radiation pattern or input impedance of the antenna. This study is confined to the properties of trap-loaded cylindrical antennas that contain only one trap in each arm. The effect of the length of the outer section, length of the inner section, diameter of the cylinder and characteristic impedance or inductance-capacitance ratio of the trap on the input impedance, radiation pattern, and current distribution were studied both experimentally and with the aid of two numerical solutions of an integral equation for the current distribution. The conclusions drawn from this study are that the design procedure for the multiband trap antenna described by Greenberg [1], adjusting the antiresonant frequency of the trap to control the upper resonant frequency, is indeed valid. Graphs suitable for designing trap antennas using this procedure are available in this paper. Furthermore, it is shown that the characteristic impedance or inductance-capacitance ratio of the trap can also be adjusted to vary the lower resonant frequency of the antenna. Design graphs using this procedure are also available in this paper. This study also showed that a relatively wide range of upper to lower antenna resonant frequency ratios can be obtained while still maintaining radiation patterns and input impedances close to those of a half-wave dipole at both frequencies. Graphs are available showing the tradeoff in pattern shape and input impedance that must be made to obtain resonant frequency ratios other than 2 to 1. It was discovered that the trap antenna, sometimes called a Franklin array, must be operated somewhat below the nominal design frequency or have the spacing between traps shortened somewhat, for it to have a radiation pattern similar to a collinear array of half-wave dipoles. Furthermore, the thicker the antenna, the more pronounced this effect is. While the nominal design was discovered to give an input impedance nearly resistive and near 70\Omega (for a dipole), any of the aforementioned modifications resulted in a nonresonant highly capacitive input impedance.

コーリニアアンテナの指向性

コーリニアアンテナの指向性

A SOLUTION OF THE DIPPING INTERFACE PROBLEM USING THE SQUARE ARRAY RESISTIVITY TECHNIQUE*

AbstractApparent resistivity measurements with the square array technique in the vicinity of a dipping interface have the advantage over collinear array methods that they are less dependent on orientation of the array.In order to exploit this, existing potential solutions for the dipping interface problem have been adapted for the computation of apparent resistivities over such a feature using a square array.Comprehensive interpretation techniques covering this problem are given and the limitations imposed by residual array orientation effects are discussed.

Geochemical-isotopic characteristics and K-Ar ages of magmatic rocks from Hundar valley, Shyok Suture Zone, Ladakh

DOI = 10.3126/hjs.v5i7.1229 Himalayan Journal of Sciences Vol.5(7) (Special Issue) 2008 p.18

Antennas for Radio Astronomy in the Metre-Wavelength Region at Ahmedabad

The paper describes three antenna arrays used in conjunction with receiving and recording apparatus for some of the solar radio astronomy and ionospheric research problems at the Physical Research Laboratory, Ahmedabad.Three pairs of cross-polarized rhombic antennas have been constructed to record the dynamic spectra of solar radio bursts covering the frequency range of 40–240 MHz. These are equatorially mounted and driven by a common synchronous motor to follow the sun continuously for about ±4 hours around the local noon.A steerable broadside collinear array of 16 half wave dipoles backed by a reflector has been constructed for radio star scintillation studies at 110 MHz. This array is also equatorially mounted and can be used to follow a radio source continuously.A simple radio interferometer, operating at 110 MHz, consisting of two Yagi antennae spaced 10 wavelengths apart has been constructed. This will be used for both the solar as well as radio star scintillation work.The effective areas, matching ...

Acoustic Imaging in a Turbid Underwater Environment

Theoretical and experimental studies are presented concerning underwater acoustic imaging in general with particular emphasis on acoustic visualization in highly turbid water. A derivation is made of the relationship between image-plane and object plane pressure distributions in an acoustic imaging system embodying a single spherical lens, and the theory is applied to both diffusely and specularly reflecting objects. The attenuation and scattering coefficients of sea water containing various ocean-bottom sediment suspensions are determined; it is found that for an acoustic frequency of 2.5 MHz (employed in the experimental work), several hundred parts per million suspended sediment concentration effects an acoustic attenuation twice that of sea water alone. A method for underwater acoustic image conversion is described which involves a sampled matrix of piezoelectric elements. Two novel switching techniques are discussed for sequentially connecting with high selectivity the various sensor elements to the output terminal. Typical shadow, focused shadow, and backscatter acoustic images are displayed that were obtained with a 100-element collinear version of the image-conversion system. The collinear array has a sensitivity threshold of better than 10−10 W/cm2 and a resolution on the order of 1.5 mm. Some of the images which are presented were taken at a range of approximately 4 m in water containing several hundred parts per million of suspended diatomaceous earth of micron particle size.

The field pattern of a long antenna with multiple excitations

The field pattern of an asymmetrically driven long antenna is obtained by the Wiener-Hopf procedure which was used by Wu [1] to calculate the field pattern of a center-fed dipole. The present analysis gives a formula which is algebraic in form and involves no numerical integration. The field pattern of a long antenna with multiple excitations or loadings can be obtained by superposition. The theory is compared with Altshuler's experiment [2] on resistor-loaded traveling-wave antennas and agreement between theory and measurement is found to be good. Application of the present result to field pattern synthesis is possible. For instance, it is known that a traveling wave of current may be produced on a center-driven dipole antenna of finite length when two suitable loads are placed symmetrically at about quarter-wavelength from its ends [2], [3]. A traveling-wave antenna tends to radiate power in an end-fire direction. On the other hand, the field pattern can be made broadside, as is shown in this paper, when the generators and the loads are re-arranged. These facts seems to suggest that a long antenna may be controlled to radiate power in any desired direction by adjusting the values and the positions of its loadings. Due to the simplicity of the formula involved, field patterns can be calculated and plotted or displayed by a computer in a short time as a function of the position of the generator. By inspection and by trial and error, desired field pattern can be obtained when appropriate individual field patterns are superimposed. It may be worthwhile to note that in this procedure the driving voltages and the locations of the generators are found so as to give certain desired pattern, the current distribution on the antenna does not have to be found first. However, the current may be found by using a simple formula derived by Shen, Wu and King [4] after the voltages and locations of the generators have been determined. The proposed method of field pattern synthesis is an alternative to the usual approach in which collinear arrays are used. One of the advantages of the present long antenna theory is that the complicated problem of mutual coupling effects between elements of an array is automatically taken into account. Furthermore, a simple and accurate formula of field pattern of a long antenna is readily available. Besides, a long antenna is a continuous structure and does not have gaps which exist between elements of a collinear array. The absence of such gaps permits coaxial feed lines to run out inside the antenna and thus simplifies the external structure of feeding networks. Two examples are shown in this paper to demonstrate the fact that long antenna can be made to radiate power in broadside direction if appropriate driving voltages are chosen. The result is compared with ideal field patterns of collinear arrays.

Infinite phased dipole array

By means of a Poisson sum formula and an integral-equation technique, an accurate solution for an infinite phased dipole array is obtained. The elements of the array are spaced uniformly and are excited with increasing phases. The technique can be applied to an infinite collinear array and to an infinite planar array either in free space or over a ground plane. The integral equation is solved both by a Fourier method and by an approximate five-term procedure. It is found that the latter is as good as the former. The current distributions and the active admittances are investigated.

Properties of a cylindrical antenna in an infinite planar or collinear array

A solution is given for the active impedance and current distribution on a cylindrical antenna in a uniform, infinite, planar, or collinear array. The analysis is applicable to the case in which the distance in the collinear direction between the ends of adjacent elements is small. The current distribution on the collinear array is found by relating the antenna current and electric-field variation on the cylindrical surface of infinite length which contains the array. This analysis is then extended to consider a planar array. Results obtained are applicable to any combination of element length and array phasing, for arrays with or without a ground plane. Comparisons with other investigations based upon sinusoidally distributed currents reveal substantial discrepancies for some configurations.