Resonant vibrations of shrouded blades with differing frequencies with clapper interference

We present the results of an experimental study of the influence of detuning of the frequencies of pairwise shrouded blades with clapper interference on their resonant vibrations. It is shown that both with the presence of clapper interference and with clapper clearance the appearance of the dangerous antiphase vibration mode of the paired blades is possible as a consequence of detuning of their frequencies. This mode is characterized by considerable increase of the vibratory stress level of the blades in comparison with the inphase vibrations.The study was carried out under the State Scientific-Engeneering Programme Improving the Reliability and Service Life and Eluninating Catastrophoic Failure of Vascular Gas Tubeline Engines.Translated from Problemy Prochnosti, No. 11, pp. 45–49, November, 1994.     

Steady-state transverse vibrations of compound rectangular orthotropic plates

A method is proposed for examining the steady-state vibrations of a compound orthotropic plate under a transverse load. The small-parameter method is used. A numerical study is presented for a plate consisting of three bands. The deflection at the center of the plate is presented as a function of the loading frequency.Translated from Problemi Prochnosti, No. 7, pp. 67–70, July, 1994.     

On the steady-state transverse vibrations of a cracked spherical shell

Using an integral formulation, the problem of a spherical shell containing a through crack of length 2c and subjected to periodic transverse vibrations of frequency is solved for the in-plane and Kirchhoff bending stresses. The usual inverse square root singular behavior characteristic to crack problems is recovered. Furthermore, it is found that the transverse vibrations reduce the stresses in the vicinity of the crack tip, except when the forcing frequency reaches the natural frequency of the uncracked shell in which case they become infinite.

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Zusammenfassung Das Problem einer sphärischen Hülle, mit einem sich über die gesamte Dicke der Hülle hinziehenden Riß der Länge 2c, welche Querschwingungen mit einer Pulsierung unterworfen ist, wurde für die Fälle von koplanaren and von Kirchhoff-Biegebeanspruchungen mit Hilfe einer Integralformulierung gelöst. Hierbei ergab sich wiederum das fur Riß-probleme charakteristische Gesetz der umgekehrten Quadratwurzel.Außerdem zeigte sich, das Querschwingungen die Spannungen in der Umgebung der Rißspitze vermindern, ausgenommen der Fall, wo die Frequenz der aufgezwungenen Schwingung mit der Eigenfrequenz der unbeschädigten Hülle übereinstimmt, wo sie dann ins Unendliche ansteigen.

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Résumé On analyse le problème de l'enveloppe sphérique ayant une fissure de longeur 2c de part en part de son épaisseur, et sujette à des vibrations transversales de pulsation ; on résoud ré problème à l'aide de fonctions intégrales, pour les contraintes coplanaires et les contraintes de flexion de Kirchhoff.On retrouve le comportement singulier habituel d'ordre 1/2, caractéristique des problèmes de fissuration. En outre, on trouve que des vibrations transversales ont tendance à réduire les contraintes au voisinage de l'extrémitée des fissures, sous réserve que leur fréquence atteigne la fréquence naturelle de l'enveloppe non fissurée; dans ces conditions les contraintes deviennent en effet infinies.

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List of Symbols and Notations c half crack length - D Eh ³/[12(1 – v ²)] = flexural rigidity - E Young's modulus of elasticity - F (x, y, t), (x,y) stress functions - ^(c)(x,y) complementary stress function - G shear modulus - h thickness - K _n modified Bessel function of the third kind of order n - L _i kernels as defined in text - m ₀ constant as defined in text - M _x ^(c) , M _y ^(c) , M _xy ^(c) complementary bending forces - M _x ^(p) , M _y ^(p) , M _xy ^(p) particular bending forces - n ₀ constant as defined in text - N _x ^(c) , N _y ^(c) , N _xy ^(c) complementary membrane forces - N _x ^(p) , N _y ^(p) , N _xy ^(p) Particular membrane forces - N _n Newman function of order n - q(x, y, t), q(x, y) internal pressure - r - R radius of curvature of the shell - R - t time variables - U(s–), U(–s) the unit step function - V _y equivalent shear - W(x, y, t), (x, y, t) displacement functions - ^(c)(x,y) complementary displacement function - dimensionless rectangular coordinates - X, Y, Z rectangular cartesian coordinates     

Resonant frequencies of a fluid in containers with internal bodies

A number of problems are solved for the resonant frequencies of oscillation of a fluid in rectangular or circular containers having internal bodies such as surface or bottom-mounted vertical blocks or circular apertures in the top surface. The variation of these frequencies with the dimensions of the bodies is obtained. The method uses matched eigenfunction expansions and Galerkin expansions to derive explicit forms for the elementsS _ijof a 2×2 matrix required in the course of the solution. An approximate formula for an arbitrary-shaped body in a container which gives good agreement with the more accurate Galerkin approach is used to solve the resonant frequencies when the internal body is a submerged cylinder.     

Resonant frequencies of Fabry-Perot interferometers with ultrathin mirror spacings

Fabry-Perot interferometers (FPIs) with multilayer dielectric mirrors and mirror spacings as low as 0.7% of the operating wavelength are studied. It is shown how these low-order FPIs are affected by the phase dispersion characteristics of multilayer dielectric mirrors. Because experimental results in the optical regime are extremely difficult to obtain, radio frequency experiments are performed with coaxial cable FPI structures. Experimental results show excellent agreement with theory. These phase effects in FPIs with ultrathin mirror spacings are of great interest in the design of tunable microcavities with possible applications in optical communications.     

Hygroscopic properties of magnetic recording tape

Relative humidity has been recognized as an important environmental factor in many head-tape interface phenomena such as headwear, friction, staining, and tape shed. Accordingly, the relative humidity is usually specified in many applications of tape use, especially when tape recorders are enclosed in hermetically sealed cases. Normally, the relative humidity is believed regulated by humidification of the fill gas to the specification relative humidity. However, this study demonstrates that the internal relative humidity in a sealed case is completely controlled by the time-dependence of the hygroscopic properties of the pack of magnetic recording tape. Procedures for the humidity conditioning of sealed cases must be established on the basis of the tapes' hygroscopic properties, and not on humidification of the fill gas. Without taking the tape into account, the final, stabilized, relative humidity can be significantly different from the specification requirement. Additionally, this same study finds differences in the hygroscopic properties of the same brand of tape, which apparently results from aging, and which may have significance on the long-term humidity-regulating behavior in a sealed case, and on the occurrence of head-tape interface phenomena from the long-term use of the tape. This article presents results on the basic hygroscopic properties of tape, its humidity-regulating behavior in a sealed case, and includes a theoretical commentary on the relative humidity dependence of head-wear by tape.     

Resonant frequency function of thickness-shear vibrations of rectangular crystal plates

The resonant frequencies of thickness-shear vibrations of quartz crystal plates in rectangular and circular shapes are always required in the design and manufacturing of quartz crystal resonators. As the size of quartz crystal resonators shrinks, for rectangular plates we must consider effects of both length and width for the precise calculation of resonant frequency. Starting from the three-dimensional equations of wave propagation in finite crystal plates and the general expression of vibration modes, we obtained the relations between frequency and wavenumbers. By satisfying the major boundary conditions of the dominant thickness-shear mode, three wavenumber solutions are obtained and the frequency equation is constructed. It is shown the resonant frequency of thickness-shear mode is a second-order polynomial of aspect ratios. This conforms to known results in the simplest form and is applicable to further analytical and experimental studies of the frequency equation of quartz crystal resonators.     

Orientation process of acicular oxides in the magnetic tape layer

The orientation of acicular particles in the active layer of a magnetic tape is presently a usual technological process applied in magnetic tape production. The theory of this process is dealt with. A mathematical model is deduced, describing the behavior of an isolated agglomerate of acicular particles in an external magnetic field and the change of its microstructure, i.e., the orientation of acicular particles in the agglomerate. The term for the density of probability ω(α) of the angle distribution α of the longer particle axes in the orientated agglomerate is also deduced. Also the approximate relation between the orientation degree, defined by the mean quadratic deviationsof the angles α of the particular particles and by the bevel values γ of the deformed agglomerate, is shown. It appears that, besides the orientation by means of the external magnetic field, it would also be possible to orientate the magnetic suspension by other methods.     

Free transverse vibrations of cracked nanobeams with surface effects

The flexural vibrations of cracked micro- and nanobeams in the presence of surface effects are studied. The cracked-beam model is set up by dividing the classical cracked beam element into two segments connected by a rotational spring located at the cracked section. This model promotes a discontinuity in bending slope, which is proportional to the second derivative of the displacements. Numerical examples demonstrate the effects of beam length, and crack position and severity on the calculated values of natural frequencies of an anodic alumina nanowire in the presence of surface effects. Limiting cases are considered and good agreements with the data available in the literature are obtained.     

Kinetics of the humid aging of magnetic recording tape

The kinetics of the hydrolysis of polyester urethane binders of magnetic recording tape is described. Kinetic data were generated from measurements of acetone-extractable hydrolyzed binder products versus time for various humidity-temperature environments. These data can be described by a linear, single product, reversible rate equation. This equation, coupled with measurements on the effect of hydrolysis on recorded tape performance, is used to predict proper environmental storage conditions for magnetic tape.     

The measurement of abrasiveness of magnetic tape

Magnetic tapes differ substantially in abrasiveness and consequent effect on head life. Logically, the consumer has expressed a need for a means to evaluate this property. In response to this demand, a number of articles and suggested test methods have appeared. The natural tendency of these offerings has been toward tests that are attractively economical of tape, time, and equipment. Such tests often involve the use of wear mechanics and geometries that are quite alien to practical tape usage. The purpose of this paper is to present evidence that efforts toward economy can be unexpectedly costly in terms of test validity. Using a test format that identifies closely with customer usage patterns, effects are shown for parameters controlled, perhaps involuntarily, by the consumer. These include contact pressure, tape speed, metal surface, and relative humidity. The effect of relative humidity, alone, is very profound. There is also a surprising degree of interaction between the relative humidity level and the type of metal being worn. The behavior of pole-piece metals is diametrically opposite to that of other structural and shielding components of a head, such as copper and aluminum, in this regard. The results of these parameter studies have been used to determine limitations that must be placed upon any valid field test for abrasiveness. These limitations appear to prohibit any field test which is very economical of tape and time. However, one possible field test design is proposed, within the limitations imposed by this study, which is relatively modest in equipment requirement and will give results in which one can justifiably have confidence.     

Role of transverse magnetic field in the capacitive discharge

The influence of magnetic field on the plasma which is one of the oldest problems in plasma physics and remains of great interest in plasma fusion studies, recently has been an important problem in many plasma discharge used in processing semiconductor materials, because the application of a magnetic field results in enhancement of some desirable features of specific plasma sources. In this paper, the transverse magnetic field effects on the radio frequency capacitive discharge of low and intermediate gas pressure (1.33 Pa∼40.00 Pa) are reviewed to clarify the role of the magnetic field in the capacitive discharge. Lots of physical phenomena induced by transverse magnetic field, such as power dissipation mode transition, low energy electron heating/cooling, axial variation of electron density and temperature and E × B drift are presented and analyzed. This article is expected to provide qualitative insight to understand the role of magnetic field in the capacitive discharges.