摘要:

This paper deals with eddy currents in bounded plane conductors. Specifically, we are concerned with the semi‐infinite plane sheet and a conducting disk. The eddy‐current distribution in a perfectly conducting sheet or disk due to a magnetic monopole source is obtained by a technique due to Sommerfeld. Sommerfeld's analysis for the disk is incomplete, but we have completed the derivation for this geometry. The eddy‐current decay in a semi‐infinite sheet of finite conductivity is solved by an approximate technique. The results are used to calculate lift, drag, and transverse forces on a magnetic monopole moving parallel to the edge of a semi‐infinite sheet of finite conductivity.

ISSN:0021-8979    

DOI:10.1063/1.1659742

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The potential distribution in cyclotron‐type gaps with liner (outer electrodes at ground potential) is determined via Schwarz‐Christoffel transformation, as well as by computer analysis (relaxation method). First‐order focusing formulas for both static, as well as time‐varying, potentials are derived. In addition exact calculations were carried out by direct numerical integration of the equations of motion with a computer program. The numerical data permitted an accurate evaluation of the validity of the analytical approximation, as well as further improvement of the theoretical formulas. Focusing relations are presented in a generalized form which shows the scaling laws and is readily applicable to different types of particles, energies, or lens geometries. As an example, the theory is applied to the axial motion of ions in a cyclotron.

ISSN:0021-8979    

DOI:10.1063/1.1659743

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

An approximate one‐dimensional theory is derived for thin crystal plates or bars with narrow rectangular cross section, and for cases in which the stiffness matrix of the crystalcijreferring to the plate axes exhibits monoclinic symmetry. A set of five equations of motion is separated into two groups: the extensional, width‐length flexural, and width‐shear motion; and the transverse shear and width‐twist motion. Closed form solutions of coupled extensional, flexural, and width‐shear vibration are obtained for thin rectangular plates with free edges. Calculated resonant frequencies as a function of length‐to‐width ratio of the plate are compared with detailed measurements by Spears on +5° X‐cut quartz plates. For the use in design, explicit algebraic formulas for predicting extensional and flexural frequencies are obtained in terms of elastic stiffnesses, density, and width‐to‐length ratio of the plates.

ISSN:0021-8979    

DOI:10.1063/1.1659744

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The three nonlinear coefficientsd31,d22, andd33that describe optical second‐harmonic generation with LiNbO3have been determined for crystals pulled from melts with Li/Nb atom ratios, (Li/Nb)m, of 0. 852, 0. 946, and 1. 083. The coefficientsd22andd33were found to be insensitive to the melt composition whereasd31increased by about 50&percent; as (Li/Nb)mwas increased from 0. 852 to 1. 083. These results suggest a marked Curie temperature dependence of the difference between the two Nb&sngbnd;O bond nonlinearities that give rise to thed's for LiNbO3.

ISSN:0021-8979    

DOI:10.1063/1.1659746

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The response of a periodic plate‐laminated composite to finite, dilatational stress waves has been investigated both experimentally and analytically. The composite was constructed of ten bilaminates oriented so that the stress wave propagated normal to the plane of the plates. The experimental results were compared to the results of a previous study, to the calculations of two wave‐propagation computer programs, and with a model in which the composite was treated as a homogeneous medium for which a stress‐relaxation relation was assumed. From these comparisons, the effects which influence the form of the stress wave were deduced. For the composite configuration used in this study and at a stress level of less than 12 kbar, the effects are geometric dispersion which includes the resonance resulting from the periodicity of the configuration, debonding, material nonlinearities, and viscosity.

ISSN:0021-8979    

DOI:10.1063/1.1659747

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

Based on assumption that the density of the material behind the shock front varies as a power function of the radial position, the equations of motion of a viscous, compressible fluid are solved analytically for the flow field in a spherical target which is impacted at hypervelocity by a spherical projectile. Good comparisons are obtained between the present solutions for velocity distribution and normal stress and various available experimental data as well as with another theoretical solution. The influence of viscosity of the material, which is assumed to be constant, on the velocity distribution and normal stress behind the shock is found to be significant after the initial hydrodynamic stage of the impact process.

ISSN:0021-8979    

DOI:10.1063/1.1659748

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

Shock deformation of Fe&sngbnd;Mn alloys up to 14 wt&percent; Mn results in a shock‐induced phase transformation. It has been shown that bcc martensite with manganese in the range 4–16 wt&percent; transforms to a stable close‐packed phase under pressure without the occurrence of reversion. The addition of manganese to iron also decreases the transition pressure from 133 kbar for pure Fe to less than 70 kbar for Fe&sngbnd;14Mn. X‐ray diffraction, electron‐probe microanalysis, electron microscopy, and density results indicate that for the Fe&sngbnd;4Mn and Fe&sngbnd;7Mn alloys, the fcc phase has been stabilized after shock deformation, while the &egr; phase has been stabilized for the Fe&sngbnd;14Mn alloy. Saturation magnetization studies have detected a residual reduction in magnetization due to the retainment of the high‐pressure phase.

ISSN:0021-8979    

DOI:10.1063/1.1659749

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

Deformation twinning has been observed in shock‐loaded samples of heat‐treated Ferrovac E iron at peak stresses from 3 to 16 kbar. In this range, the volume fraction of twins increases monotonically from zero to approximately 4&percent;. In instrumented transmitted‐wave measurements stress relaxation was observed behind the elastic precursor for propagation distances of 12 mm or greater, but not at smaller distances. An analytical description of dynamic deformation twinning which adequately describes experimental observations on shock‐wave propagation in Ferrovac E iron is proposed. This analysis is based on models for the growth of twin platelets combined with the equation &ggr;=k&agr; relating the plastic strain &ggr; to the twinning shearkand the volume fraction of twins &agr;. Dynamic deformation twinning in impact‐loaded solids appears to be fairly well established both from experimental and analytical points of view and certainly must be considered as a possible physical mechanism in the description of plastic flow at high strain rates.

ISSN:0021-8979    

DOI:10.1063/1.1659750

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

A simple model for simultaneous viscous flow and diffusion of gases through small apertures has been formulated. Data obtained with a fine capillary and with a pinhole are in good agreement with the theoretical predictions. The experimental approach involving continuous flow of test and carrier gas past either side of the aperture is useful for the determination of the sensitivity of trace gas detectors.

ISSN:0021-8979    

DOI:10.1063/1.1659751

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The craze‐initiation criteria for craze‐prone glassy polymers are examined with a model test method. In this method a prismatic sample of polystyrene with an embedded steel ball is subjected to a simple tension until crazing takes place around the interface. Stress analysis showed that various published craze‐initiation criteria will predict the appearance of the first crazes at different locations on the interface in such samples. Thus by comparing the experimental and analytical results it is possible to determine from the actual craze‐initiation locations which of the existing theories is likely to explain the craze initiation. The study revealed that the principal strain criterion gave the best prediction while the dilation criterion yielded the least likely result. The polystyrene samples with an embedded rubber ball were also tested and the data compared with the analytical results. In this case all criteria predict correctly that crazing will first occur at the equator of the rubber ball, indicating that the simple tension test of rubber ball samples is not suitable for determining the dominant craze‐initiation mechanism. Comparison of the crazing behavior in the rubber ball sample and the steel ball sample revealed that the crazes which developed around the rubber ball were more stable than those developed around the steel ball. The above observation may explain why harder inclusions are not as effective as rubber inclusions in toughening the glassy polymers. The incipient craze angles were examined and found to be in agreement with the general observation that the crazes form in the direction normal to the major principal stress.

ISSN:0021-8979    

DOI:10.1063/1.1659752

出版商:AIP    

年代:1971

数据来源: AIP