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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 24 (1953), S. 104-106 
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Summary Brunt's simple expression for the diurnal variation of the surface temperature of the ground at the equinox is extended to any conditions. It is found that the time lag after noon of the maximum temperature varies from between 1.9 to 2.9 hours according to latitude and season.
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  • 2
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Summary Numerical results are given which show the way in which thc Curie temperature moves inwards from the margin during the cooling of a thick intrusive sheet. The time taken to move from the margin to the centre varies as the square of the thickness of the sheet, being about 6500 years for a sheet 1000 m thick on reasonable assumptions as to the thermal properties of the material. This implies that the secular variation of the Earth's magnetic field over periods of time of 1000 years or more may be studied by measuring the directions of magnetisation at a series of points across the thickness of such a sheet. Some measurements on a Tasmanian sill about 430 m thick of Jurassic or Cretaceous age suggest a change from maximum to minimum inclination in a time of about 200 years. Since the margins of the sill are not available this figure may be considerably in error but the results suggest the general practicability of the method.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 67 (1997), S. 247-259 
    ISSN: 1432-0681
    Keywords: Key words uncoupled contact ; plane elasticity ; Cattaneo-Mindlin principle ; elastic friction ; singular integrals.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Nonrotating half-planes in contact under oblique loading are investigated in this paper. The solution is based on the influence integrals of the Flamant solution. The problem is determined by two integral equations for the normal and tangential stresses, which are uncoupled for special cases, as bodies of similar material in contact. In order to simplify the singular integrals, the method of superposition of flat punches is used. The result for the symmetric case is almost identical with the axisymmetric solution. For polynomial profiles of the form x s , the Muskhelishvili potentials can be written in terms of a complex hypergeometric function. The interior stress field is illustrated for an example.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 69 (1999), S. 181-203 
    ISSN: 1432-0681
    Keywords: Key words granular material ; generalized Hertz contact ; elastic friction ; nonlinear elasticity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Mechanical behavior of dense packing spheres with small irregularities is investigated in this paper. A generalization of the hertzian contact model for surfaces of the form x k yields a normal contact force F n , which is proportional to ζ1+1/ k , with the normal displacement ζ. For oblique forces, the frictional force can be calculated, [10]. Different load cases are explained in detail. It is shown that the stress-strain curve during initial loading of the packing is identical with the force-displacement relation at the contact point, using an appropriate constant. The results for uniaxial loading, unloading and reloading are illustrated. As experimentally observed, the axial pressure in unloading is smaller than during loading, while the lateral pressure increases. The stress-strain relation is compared with well-known empirical relations of rock and soil mechanics, and the wave velocity for spherical irregularities agrees with earlier geomechanical theories for random packing of smooth spheres.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 43 (1959), S. 148-158 
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Summary The conditions for sliding over artificial joint surfaces have been studied experimentally by cutting rock cylinders at various angles to their axes and studying slip over these surfaces in a triaxial testing apparatus. The types of joint used were: (i) filled with plaster to simulate a soft joint filling, (ii) bare surfaces ground approximately flat, and (iii) natural surfaces across which shear failure had taken place. The results agreed reasonably well with the simple theory for a constant coefficient of friction. Measured coefficients of friction lie in the range 0.5–0.8 and differ by surprisingly little between the various surfaces. The surfaces across which sliding has taken place exhibit interesting slickenside phenomena. Subsidiary failures frequently occur which cut across the joint surfaces.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 63 (1993), S. 402-412 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es werden die Phänomene untersucht, die beim Kontakt elastischer Kugeln unter der Einwirkung von Kräften mit veränderlicher, unidirektionaler Tangentialkomponente mit veränderlichem Vorzeichen und veränderlicher Normal-komponente auftreten. Das Kontaktgesetz beruht auf der von H. Hertz [3] eingeführten Annahme, daß sich beide Körper physikalisch wie elastische Halbräume verhalten. Wir nehmen konstante Spannungsrichtungen im Gleitgebiet an, um mit Hilfe sogenannter Cattaneo-Mindlin-Funktionen das tangentiale Randwertproblem zu lösen. Die Spannungsverteilung der Cattaneo-Mindlin-Theorie [2], [8] ist rotationssymmetrisch und hat einen typischen Knickpunkt am Rand des Haftgebiets an der Stelle ϱ=a 1 *, füra 1 *〈a 1, mit dem Radiusa 1 * des Haftgebiets und dem Radiusa 1 des Kontaktgebiets. Die allgemeine Lösung des tangentialen Kontaktproblems kann als eine Summe von Cattaneo-Mindlin-Funktionen dargestellt werden. Die geeignete Überlagerung von zwei cattaneo-Mindlin-Funktionen ergibt eine neue Cattaneo-Mindlin-Funktion, was die Berechnung der Kraft und der Verschiebung beträchtlich vereinfacht. Wir leiten eine Formel für die Kraft-Verschiebungs-Beziehung bei allgemeinen Belastungsgeschichten her, die durch Differentiation auf die Nachgiebigkeiten von Mindlin & Deresiewicz [9] reduziert werden kann. Im Gegensatz zu Mindlin & Deresiewicz hängt unsere Formel nur von den Punkten momentanen HaftensP i (für 1≦i≦N−1) und von den aktuellen Verschiebungen ξ N und ζ N in tangentialer und normaler Richtung des anfänglichen Kontaktpunktes ab, was die Lösung vereinfacht. Es ermöglicht auch eine Verallgemeinerung für schiefe Belastungsgeschichten mit elliptischen Kontaktgebieten und Tangentialkräften mit veränderlicher Richtung [4]. Schließlich wird ein Algorithmus angegeben, welcher die notwendige Zahl von Cattaneo-Mindlin-Funktionen bestimmt.
    Notes: Summary An investigation is made of the phenomena occurring at the contact of elastic spheres, subjected to forces with varying tangential component, in one direction, with changing sign, and varying normal component. The contact law is based on the assumption, introduced by H. Hertz [3], that both bodies behave physically like elastic half-spaces. We assume constant stress directions in the slip area in order to use so-called Cattaneo-Mindlin functions to solve the tangential boundary value problem. The stress distribution of the Cattaneo-Mindlin theory [2], [8] is rotational symmetric and has a typical break at the border of the stick area at ϱ=a 1 * fora 1 *〈a 1, with the radiusa 1 * of the stick area and the radiusa 1 of the contact area. The general solution of the tangential contact problem can be written as a sum of Cattaneo-Mindlin functions. The appropriate superposition of two Cattaneo-Mindlin functions yields a new Cattaneo-Mindlin function, which simplifies the calculation of the force and the displacement. We will arrive at a formula for the force-displacement relation of general load-histories, which can be reduced to the compliances of Mindlin & Deresiewicz [9] by differentiation. In contrast to Mindlin & Deresiewicz our formula depends only on the points of instantaneous adhesionP i , for 1≦i≦N−1, and the current displacements ξ N , ζ N in tangential and normal direction of the initial contact point, which simplifies the solution. It also allows a generalization for oblique load-histories with elliptical contact areas and tangential forces in varying directions [4]. Finally an algorithm is given, which determines the essential number of Cattaneo-Mindlin functions.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 64 (1994), S. 235-248 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht In diesem Artikel wird der Stoß zweier geometrisch und materiell ähnlicher Kugeln untersucht, welche um die gemeinsame Normale ihres Kontaktgebietes rotieren. Die Lösung des statischen Kontaktproblems, bei welchem die Kugeln durch eine konstante Normalkraft zusammengedrückt und anschließend durch ein monoton steigendes Torsionsmoment um die Kontaktnormale belastet werden, wurde von Lubkin gefunden. Die Überlagerung der Lubkin-Funktionen für unterschiedliche Kontaktgebiete ergibt das allgemeine Kontaktgesetz für eine Folge endlicher Normalverschiebungs-und Torsionsinkremente. Die Drehung am Stoßende erhält man durch numerische Integration der Drallgleichung und des Kontaktgesetzes. Die Nassi-Shneiderman-Diagramme des Kontaktalgorithmus und des Stoßprogramms werden abgebildet. Einige Ergebnisse werden vorgestellt und mit einer asymptotischen Theorie für vollständiges Haften und vollständiges Gleiten verglichen.
    Notes: Summary In this article, the collison of two geometrically and materially similar elastic spheres, which are rotating around the common normal of their contact area, is analysed. The solution of the static problem, when the spheres are pressed together by a constant normal force and are then subjected to a monotonously increasing torsional couple about the contact normal, has been found by Lubkin. Superposition of Lubkin's solutions for varying contact areas yields the general contact law for finite sequences for normal and torsional displacement increments. The torsional rotation at the end of impact is obtained from numerical integration of the angular equation of motion and the contact law. The Nassi-Shneiderman diagrams of the contact algorithm and the impact algorithm are presented. Some results are plotted and compared with an asymptotic theory for complete adhesion and complete sliding in the contact area.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 65 (1995), S. 478-487 
    ISSN: 1432-0681
    Keywords: Key words Contact problem of elasticity ; superposition ; flat punch solutions ; annular sliding ; stick area.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  Two axi-symmetric bodies are pressed together, so that their axes of symmetry coincide with the contact normal and the normal force is held constant. A small torque about the contact normal or a small tangential force is applied. For bodies of equal material, the normal and tangential stress states are uncoupled, and can be solved separately. The surfaces of the bodies are thought as a superposition of infinitesimal rigid flat-ended punches. Consequently, the normal stress distribution can be calculated as a summation of differential flat punch solutions. A formula results, which is identical with the solution of Green and Collins. After application of a torque an annular sliding area forms at the border of the contact area. For reasons of symmetry, the common displacement of the inner stick area must be a rigid body rotation. Similarly to the normal problem, the solution can be thought as a superposition of rigid punch rotations. The tangential solution can be derived analogically, in form of a superposition of rigid punch displacements. The present method also solves the problem of simultaneous normal and torsional or tangential loading with complete adhesion. As an example, Steuermann’s problem for polynomial surfaces of the form A 2 n r2 n is solved. The solutions for constant normal forces can be used as basic functions for loading histories with varying normal and tangential forces.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 65 (1995), S. 478-487 
    ISSN: 1432-0681
    Keywords: Contact problem of elasticity ; superposition ; flat punch solutions ; annular sliding ; stick area
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Two axi-symmetric bodies are pressed together, so that their axes of symmetry coincide with the contact normal and the normal force is held constant. A small torque about the contact normal or a small tangential force is applied. For bodies of equal material, the normal and tangential stress states are uncoupled, and can solved separately. The surfaces of the bodies are thought as a superposition of infinitesimal rigid flat-ended punches. Consequently, the normal stress distribution can be calculated as a summation of differential flat punch solutions. A formula results, which is identical with the solution of Green and Collins. After application of a torque an annular sliding area forms at the border of the contact area. For reasons of symmetry, the common displacement of the inner stick area must be a rigid body rotation. Similarly to the normal problem, the solution can be thought as a superposition of rigid punch rotations. The tangential solution can be derived analogically, in form of a superposition of rigid punch displacements. The present method also solves the problem of simultanous normal and torsional or tangential loading with complete adhesion. As an example, Steuermann's problem for polynomial surfaces of the formA 2nr2nis solved. The solutions for constant normal forces can be used as basic functions for loading histories with varying normal and tangential forces.
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  • 10
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Description / Table of Contents: Zusammenfassung Die Absorptionsspektren von CeCl3·7 H2O, LaCl3·7 H2O, CeCl3·7 D2O und LaCl3·7 D2O wurden bei tiefen Temperaturen im Gebiet des 4 f→4 f Übergangs gemessen. Die Energieniveaus der Ce3+-Ionen in diesen Verbindungen wurden bestimmt. Desgleichen wurden aus den zwischen 4000 cm−1 und 50 cm−1 gemessenen Reflexionsspektren dieser Kristalle die infrarot-aktiven Phononenübergänge bestimmt. Einige der Energieniveaus der Ce3+-Ionen in den deuterierten Kristallen werden um etwa 10 Wellenzahlen gegen die des CeCl3·7 H2O verschoben. Diese Verschiebungen sind wahrscheinlich auf eine resonante Elektron-Phonon-Wechselwirkung in der einen oder anderen der beiden Verbindungen zurückzuführen.
    Abstract: Résumé Les spectres d'absorption de CeCl3·7 H2O, LaCl3·7 H2O, CeCl3·7 D2O et LaCl3·7 D2O ont été mesurés à basses températures dans la région des transitions infrarouges 4 f→4 f. Les niveaus d'énergie de l'ion Ce3+ en ces deux composés ont été dérivés. De même les transitions infrarouges des phonons ont été déterminées à partir des spectres de reflexion de ces cristaux mesurés entre 4000 cm−1 et 50 cm−1. Un certain nombre des niveaus d'énergie des ions Ce3+ est décalé d'environ 10 nombres d'ondes vers ceux du CeCl3·7 H2O. Ces décalages sont probablement dus à une interaction entre niveaus électroniques et états resonants de phonons dans l'un ou l'autre des deux composés.
    Notes: Abstract The absorption spectra of CeCl3·7 H2O, LaCl3·7 H2O, CeCl3·7 D2O and LaCl3·7 D2O have been measured at low temperatures in the region of the 4 f→4 f infrared transitions. The energy levels of the Ce3+-ion in these compounds have been derived. The infrared phonon transitions have also been determined from the reflection spectra of these crystals measured in the region between 4000 cm−1 and 50 cm−1. Some of the energy levels of the Ce3+-ions in the deuterated crystals are shifted for about 10 wavenumbers against those in CeCl3·7 H2O. These shifts are probably due to an interaction of the electronic levels with resonant phonon-states in one or the other of the two compounds.
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