Radial oscillations of nonhomogeneous,thick-walled cylindrical and spherical shells subjected to finite deformations

The infinitesimal breathing motions of long cylindrical tubes and hollow spherical shells of arbitrary wall thickness subjected to a finite deformation field caused by uniform internal and/or external pressures are investigated. A neo-Hookean material with a material constant varying continuously along the radial direction is used. The shell is first subjected to finite static deformations and is then exposed to a secondary dynamic displacement field. Based on the theory of small deformations superposed on large deformations, closed form expressions are obtained for the frequency of small oscillations about the highly prestressed state. Frequency versus initial deformation parameter curves are given for several nohomogeneity functions and for various wall thicknesses.     

Vergleichende Untersuchungen der Strömungsprofile und des Fließverhaltens Nicht-Newtonscher Flüssigkeiten im Rotationsviskosimeter

Übersicht Es wird die Verträglichkeit der aus drei verschiedenen Meßverfahren resultierenden Aussagen über das Fließverhalten Nicht-Newtonscher Flüssigkeiten im Couette-Spalt für die beiden Fälle untersucht, daß das Material entweder dem Ostwaldschen oder dem Prandtlschen Fließgesetz gehorcht. Für die benutzten Verfahren: 1. Ausmessung des Strömungsprofils, 2. Entspannungsmessung, und 3. Messung der Drehmomente bei konstanten Drehzahlen des Rührers, werden zweckmäßige, graphische Auswerteverfahren entwickelt, die bereits durch einen Formvergleich zwischen Meßkurven und Musterkurven eine Entscheidung zugunsten des einen oder anderen Fließgesetzes ermöglichen, wenn die Streuung der Meßdaten es zuläßt. Am Beispiel einer Tonsuspension wird gezeigt, daß eine Entscheidung über die Gültigkeit eines der beiden Ansätze jedoch auch bei größeren Streuungen der Versuchswerte gefällt werden kann, wenn man die aus den drei Verfahren resultierenden Ergebnisse auf ihre Verträglichkeit prüft.

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Summary The compatibility of the results of three different testing methods concerning the flow behaviour of Non-Newtonian liquids within the Couette-gap is examined for both cases, whether the material follows either Ostwald's or Prandtl's law of flowing. For the employed procedures: 1. Measuring of the flow profile, 2. Measuring of the torsion release, 3. Measuring of the torque of constant rotational speed of the stirrer, suitable graphical methods of valuation are developed, to decide in comparison with the form between measuring curves and master curves in favour of one flowing law or the other, provided that the scattering of test results permits it. At the example of a clay suspension it is shown that a decision concerning the validity of one of the two formulae can be given, if the results are being judged with respect to their compatibility.

     

Temperature distribution in a thin rotating disk

The problem of heat conduction in a thin rotating disk with heat input at a fixed point is considered. The disk is cooled by forced convection from its lateral surfaces. By defining a complex temperature, the temperature throughout the disk is presented as a series of Bessel functions of complex argument. Results are given for a range of rotational speeds.Nomenclature R radial coordinate - angular coordinate - a radius of disk - b thickness of disk - T temperature - T ambient temperature - rotational speed of disk - q heat flux into disk - k thermal conductivity of disk - density of disk - c specific heat of disk - h coefficient of convective heat transfer - r dimensionless radial coordinate, R/a - T* characteristic temperature, q ₀ a/ k - t dimensionless temperature, (T–T )/T* - C ₁, C ₂ dimensionless parameters defined in (3)     

New equipment for cyclic biaxial testing

Methods of achieving biaxial-stress states in fatigue tests are reviewed. A new design of equipment that produces five distinct biaxial-stress states by simultaneous direct pressurization and axial loading of thinwalled cylindrical specimens is described. Four variations of stress state are obtained by the use of two sizes of specimen and by reversal of the pressurizing connections. The fifth state is obtained by direct pressurization without axial load. The actual magnitudes of stress in the specimen are computed from the output of the load cell in the reaction frame in which the biaxial-testing device is mounted. Additional stress ratios are obtained using standard uniaxial and torsional cyclic-testing arrangements. The initial program using this equipment was to investigate the effects of biaxiality on the cyclic properties and low-cycle fatigue behavior of normalized 1018 mild steel, under fully reversed constant-amplitude strain control. Control was achieved using a servo-controlled, electrohydraulic testing system with one of the two clipon strain transducers, that were mounted on the specimen, providing the controlling electrical signal. The system allowed direct recording of the stress-strain hysteresis loops in both principal directions. The behavior of the equipment and the modes of failure of the specimens are described and some test data are presented. The range of application and limitations of the equipment for further cyclic biaxial testing are discussed.     

Flows of dilute polymer solutions through packed porous chromatographic columns

Summary We have found that diffusion of polystyrene into the micropores of packed porous chromatographic columns of a type used for size separations of macromolecules is strongly influenced by the flow rate of the polymer solution through the column and also by the macromolecular size and internal pore size of the column packing. Dilute polymer solutions (0.05 wt.% polystyrene in THF) were pumped continously through the columns (Dupont SEC). Step changes in flow rate were made and the polymer concentration in the column effluent was monitored continuously. When the flow rate was increased, the partition coefficient for polymer between mobile and stationary phase shifted toward more polymer retention in the column, as evidenced by the drop in outlet concentration for several minutes following the step change. Molecular weight, pore size and solvent effects have all been thoroughly investigated. The conclusion is that polymer molecules diffuse into the internal pores of the column packing at a flow ratedependent rate and moreover, they do so to a greater extent the larger the polymer molecule, provided they are not sterically excluded from the pores. This dynamic diffusional partitioning is clearly important in its effect on resolution characteristics of an SEC column and also sheds some light on qualitatively similar observations in polymer flooding for enhanced oil recovery.

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Zusammenfassung Es wurde gefunden, daß die Diffusion von Polystyrol in die Mikroporen von porösen Packungen chromatographischer Säulen, wie sie für die Trennung von Makromolekeln verschiedener Teilchengrößen Verwendung finden, sowohl von der Fließgeschwindigkeit der Polymerlösung durch die Säule als auch von der Größe der Makromolekeln und der inneren Poren erheblich beeinflußt werden. Verdünnte Polymerlösungen (0,05 Gew.-% Polystyrol in THF) wurden kontinuierlich durch die Säulen (Dupont SEC) gepumpt. Dabei wurde die Fließgeschwindigkeit sprunghaft geändert und die Polymerkonzentration im Auslauf kontinuierlich registriert. Wenn die Durch-flußgeschwindigkeit erhöht wurde, verschob sich der Verteilungskoeffizient der Polymeren zwischen bewegter und stationärer Phase zu höheren Polymeranteilen in der Säule hin, was durch einen Konzentrationsabfall in der ausfließenden Lösung während einiger Minuten nach dem Geschwindigkeitssprung angezeigt wurde. Molekulargewicht, Porenweite und Lösungsmitteleinfluß wurden eingehend untersucht. Dabei ergab sich, daß die Polymermolekeln in die inneren Poren der Packung mit einer fließgeschwindigkeitsabhängigen Geschwindigkeit hineindiffundieren und dies in einem um so höheren Maße, je größer die Molekeln sind, vorausgesetzt, daß sie nicht aus sterischen Gründen zurückgehalten werden. Diese dynamische diffusive Verteilung ist natürlich von Bedeutung für die Trenncharakteristik einer GPC-Säule und wirft ebenso einiges Licht auf verschiedene qualitativ ähnliche Beobachtungen beim Fluten mit Polymeren zur Ausbeutesteigerung bei der Ölförderung.

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With 8 figures and 3 tables     

Die Berechnung des Blasenwachstums beim Verdampfen von Flüssigkeiten an Heizflächen als numerische Lösung der Erhaltungsgleichungen

A numerical procedure on the basis of the Marker and Cell-method [1] was developed in order to solve the conservation equations for mass, momentum and energy for the case of bubble growth on a heating surface. This procedure was used to calculate steam bubble growth on a horizontal stainless steel heating surface under saturated pool boiling conditions at a system pressure of 1 bar and different superheatings. The essential results obtained are:

-Good agreement was found between calculations and experiments concerning bubble growth rates, bubble shape and temperature field in the liquid surrounding the bubble.

-During its growth the bubble penetrates the temperature boundary layer formed in the liquid on the heating surface, simultaneously liquid is displaced aside.

-The microlayer evaporation fraction of the total bubble growth increases with growth time from 20 % to 50%.

     

Versuche zu einem „shear-rate-blockage“-Effekt am Protoplasma zentrifugierter Gewebe

Ohne ZusammenfassungI thank Mr.Scott Blair for his answer reserving the term dilatancy for cases of real dilatation. Now it's only to wish that this terminology is used according to his Report on the principles of rheological nomenclature (Amsterdam 1949).     

The evaluation of the surface impedance in the theory of the anomalous skin effect in metals

Summary A simple method is described for obtaining series expansions for the integrals which represent the surface impedance in the theory of the anomalous skin effect in metals. The results agree with those recently obtained by Dingle¹) by means of an intuitive procedure.     

An atomistic-based continuum theory for carbon nanotubes: analysis of fracture nucleation

Carbon nanotubes (CNTs) display unique properties and have many potential applications. Prior theoretical studies on CNTs are based on atomistic models such as empirical potential molecular dynamics (MD), tight-binding methods, or first-principles calculations. Here we develop an atomistic-based continuum theory for CNTs. The interatomic potential is directly incorporated into the continuum analysis through constitutive models. Such an approach involves no additional parameter fitting beyond those introduced in the interatomic potential. The atomistic-based continuum theory is then applied to study fracture nucleation in CNTs by modelling it as a bifurcation problem. The results agree well with the MD simulations.