Ähnliche Grenzschichtlösungen zweiter Ordnung für Strömungs- und Temperaturgrenzschichten an longitudinal gekrümmten Wänden mit Grenzschichtbeeinflussung

Zusammenfassung Für die inkompressible, stationäre Strömungs- und Temperaturgrenzschicht an longitudinal gekrümmten Wänden mit Grenzschichtbeeinflussung werden unter Berücksichtigung der Glieder zweiter Ordnung, d. h. mit Berücksichtigung der Verdrängung und des metrischen Krümmungseinflusses ähnliche Lösungen angegeben. Die Lösungen erstrecken sich auf Wände, deren Krümmungk proportional zu einer Potenz der Bogenlängex ist. In dieser Familie von Wandkurven sind die Staupunktströmung an einem Zylinder und die Strömungen an Keilen mit gekrümmten Keilflanken eingeschlossen. Dabei ist der Öffnungswinkel des Keils mit dem Krümmungsverlauf der Keilflanken verknüpft.

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Similarity solutions are given for incompressible, steady hydrodynamic and thermal boundary layers on longitudinally curved walls with boundary layer interference considering second order terms i. e. allowing for displacement and metric curvature influence. The solution apply to walls with curvaturek proportional to a power of the arc lengthx. Involved in this family of wall-curves is the stagnation point flow on a cylinder and the flow along wedges with curved walls. Here, the angle of the wedge is connected to the curvature of the wedge-walls.

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Mit Unterstützung der Aerospace Research Laboratories durch das U. S. Air Force European Office of Aerospace Research.     

Ein Verfahren zur Berechnung von Eigenwertschranken mit Anwendung auf das Beulen von Rechteckplatten

Übersicht Das Verfahren von Lehmann und Maehly zur Berechnung unterer und oberer Schranken für die Eigenwerte Hermitescher Operatoren im Hilbertraum wird übertragen auf das allgemeine Eigenwertproblem eines Operators relativ zu einem zweiten. Das Verfahren führt auf ein lineares Matrix-Eigenwertproblem. Als charakteristische Schwierigkeit tritt in der Rechenvorschrift für die Matrixelemente ein inverser Operator auf. Man ersetzt ihn durch seine Truncation, und erhält so ein verallgemeinertes Verfahren zur Berechnung unterer und oberer Eigenwertschranken. Das Verfahren wird angewandt bei der Berechnung von Beulwerten von Rechteckplatten.

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Summary The procedure of Lehmann and Maehly for the calculation of lower and upper bounds to eigenvalues of Hermitian operators in Hilbert space is transferred to the eigenvalue problem of one operator relative to another. The problem is reduced to a linear matrix eigenvalue problem. It is a characteristic difficulty that one needs an inverse operator to calculate the matrix elements. The replacement of this operator by its truncation yields a generalized procedure for the calculation of lower and upper bounds to eigenvalues. The method is used in the buckling of rectangular plates.

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Gekürzte Fassung eines Teiles der Dissertation des Verfassers, eingereicht in der TH Darmstadt, 1966.     

A torsional creep apparatus

Summary This paper describes a torsional creep apparatus for the determination of the creep compliance in shear as a function of time. The instrument is suitable for the measurement of compliances below 5·10^–8 m²/N, in the time range between 1 and 10⁵ seconds. Within five minutes and with an accuracy of 1 C, the temperature of the specimen can be adjusted to any value between –175 and –200 C. From the torsional creep measurements can be calculated the dynamic shear modulus and the corresponding damping. The lowest damping, determined in this way, is several times 10^–3.

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Zusammenfassung Ein Apparat zur Messung des Torsions-Kriechverhaltens wird beschrieben. Das Instrument ist zur Bestimmung von Nachgiebigkeiten kleiner als 5·10^–5 m²/N im Zeitbereich zwischen 1 und 10⁵ Sekunden geeignet. Die Temperatur der Probe läßt sich innerhalb 5 Minuten und mit einer Genauigkeit von 1 C auf jeden Wert zwischen –175 und –200 C einstellen. Aus der gemessenen Kriechfunktion können der dynamische Schubmodul und die dynamische Dämpfung berechnet werden. Eine untere Grenze für die Dämpfung, die man auf diese Weise noch bestimmen kann, ist einige Male 10^–3.

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The work was partly sponsored by the Office of Naval Research, Washington, D. C., under contract number N 62558-3884.     

On the existence and bifurcation of minimal normal modes

Minimal normal modes (MNMs) are defined as non-linear normal modes which give a true minimum to Jacobi's Principle of Least Action. It is shown that for a certain class of two degree of freedom non-linear conservative systems, MNMs generically occur in pairs. The nature of both generic and non-generic bifurcations of MNMs is derived and illustrative examples are given.     

Unsteady state diffusion of vapour in a closed tube

Results of one-dimensional calculations for unsteady state diffusion of a vapour in a closed tube are compared to calculations (a) for unsteady state diffusion of a vapour in an open tube, and (b) for heat conduction in a finite slab and an infinite slab. In the cases of (b) the effect of the convective term in the transport equation is absent.The total pressure is calculated and differences in the two cases are explained.An experiment is described in which the pressure increase in a closed tube due to the diffusion of water vapour in dry air is measured as a function of time. The experimental results agree quite well with the theoretical predictions. The results of this investigation may be used for the experimental determination of the diffusion coefficient of a vapour in a gas and in pressure measurements in systems with an evaporating liquid.Nomenclature a thermal diffusivity - D diffusion coefficient - w mean particle velocity - g particle flux in the laboratory system - g* particle flux in a system moving with the mean particle velocity w - L length of the tube - n number density of molecules - n _vs saturation number density of vapour molecules - p pressure - p _vs saturation pressure of the vapour - t time - z distance from the liquid surface - N total quantity of evaporated liquid     

A dynamic photoelastic study of stress-wave propagation through an inclusion

A photoelastic study of the elastodynamic-stress fields around a circular, elastic inclusion (Solithane 113) embedded in an elastic plate (Hysol 4485) is presented. The edge of the plate was loaded by an explosive charge, which produced a plane, compressional stress wave of triangular shape. Isochromatic-fringe patterns were obtained, which give the maximum shear stresses, both inside the inclusion and in the surrounding medium. The principal stresses on the axis of symmetry were determined through the use of the oblique-incidence method. It was found that small tensile stresses are generated at the interface on the shadow side of the inclusion. The focusing effect inside the inclusion predicted by ray theory was not observed. Finally, the shape of the wavefront as the wave passes the inclusion was determined.     

Application of a microprocessor for acquisition of load,strain and acoustic-emission data

This paper describes an automatic system for acquisition, logging and analysis of stress, strain and acoustic-emission data. The complete system is a combination of several standard items of equipment and a newly developed intelligent data logger which has the capability to send data directly to a large-scale computer for reduction and plotting. The data logging and all interfacing with peripheral equipment are accomplished using digital electronics. The heart of the system is a four-bit microprocessor and digital cassette-tape unit. The system, which is controlled by instructions from a cathode-ray-tube terminal, has the capability to transmit data from the cassette unit to a large computer via a time-sharing aption. Typical results are presented for acoustic-emission count rate and total-count curves superimposed on stress-strain diagrams for boron/epoxy advanced composites.     

Thermohydrodynamic conditions at the peak flux of horizontal heaters in superfluid liquid helium II at zero net mass flow

Measurements of the peak flux (at the onset of film boiling) in He II are used as a diagnostic tool to investigate the non-classical thermohydrodynamics of superfluid liquid helium for horizontal heaters at zero net mass flow. Data for the single horizontal cylinder in a large pool of He II are approximately accounted for by a power law describing the dimensionless nonclassical superfluid transport number as a function of the fourth root of the dimensionless thermo-mechanical driving potential. Results for transport in narrow vertical cylinders (with insulated walls and lower end closed) are approximately described on the basis of the Gorter-Mellink transport equations. The saturation hypothesis is used which postulates local onset of boiling when vapor-liquid equilibrium is reached at the heater.     

Extremalprinzipe der Thermodynamik und Mechanik für stabile Gleichgewichtslagen von Kontinua

Übersicht In dieser Arbeit soll der Zusammenhang zwischen den Extremalprinzipien der Thermodynamik und der Mechanik für stabile Gleichgewichtszustände eines Kontinuums studiert werden. Als Nebenprodukt ergeben sich dabei zwanglos Verallgemeinerungen der klassischen Extremalprinzipe der Elastizitätstheorie (des Minimum-Energie-Prinzips und des Prinzips von Castigliano) auf multipolare und chemisch reagierende Materialien.

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Summary The aim of this paper is to study the relations between the variational principles of thermodynamics and mechanics for stable equilibrium states of a deformable body. As a by-product one obtains generalisations of the classical principles of elasticity-theory (the minimum-energy-principle and Castigliano's theorem) to multipolar and chemically reacting materials.

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Herrn Prof. Dr.-Ing. K. Klotter zum siebzigsten Geburtstag gewidmet.