On the elastodynamics of stiffened plates

Summary A method of determining the response of a stiffened elastic plate to a dynamic excitation is presented here. Green's function for such a combined system has been systematically derived based on the eigenfunctions of the system obtained through the application of Galerkin's method. With that Green's function a wide range of dynamic forcing functions can be considered.

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Zur elastodynamik versteifter platten

Übersicht Vorgestellt wird eine Methode zur Ermittlung der Antwort versteifter Platten auf dynamische Erregungen. Mit Hilfe der Eigenfunktionen des Systems, die durch Anwendung der Galerkin-Methode gewonnen werden, wird die Greensche Funktion solcher kombinierten Tragwerke systematisch hergeleitet. Damit kann ein weiter Bereich dynamischer Anregungsfunktionen behandelt werden.

     

Difference between the longitudinal Frenkel-Biot waves in water-and gas-saturated porous media

The problem of the propagation of longitudinal Biot waves in a porous medium saturated with a weakly compressible liquid (water) or a gas is considered theoretically. The frequency dependence of the phase velocities and damping coefficients is investigated numerically. It is shown that for a certain relationship between the parameters of the porous medium and the saturating fluid there is a “critical” frequency at which the properties of longitudinal waves of both kinds are identical. An analytical expression for this “critical” frequency is obtained. It is shown that for a gas-saturated porous medium, at a certain frequency, in both longitudinal waves the relative gas-matrix motion changes type. Assuming that the saturating-gas behavior corresponds to an adiabatic equation of state, an estimate is obtained for the threshold pore pressure necessary for the restructuring of the relative motion. The wave associated with matrix deformation is shown to have a high damping coefficient in a porous medium saturated with a weakly compressible liquid (water in the case considered) but to be only weakly damped in a gas-saturated porous medium.     

Numerical modeling of the single-phase Stefan problem in a layer with transparent and semitransparent boundaries

Numerical modeling of the single-phase Stefan problem in a semitransparent layer with transparent, nonabsorbing, and partially radiation-absorbing boundaries is performed. It is shown that at low temperatures of the medium, convection is a determining factor on the boundary of the irradiated sample, and at high temperatures, radiation is predominant. The absence of absorption on the boundaries of the layer leads to acceleration of the heating of the plate and considerable deceleration of melting processes. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 84–91, May–June, 2006.     

Studies on Bifurcation and Chaos of a String-Beam Coupled System with Two Degrees-of-Freedom

In this paper, research on nonlinear dynamic behavior of a string-beam coupled system subjected to parametric and external excitations is presented. The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam coupled system. The Galerkin's method is employed to simplify the governing equations to a set of ordinary differential equations with two degrees-of-freedom. The case of 1:2 internal resonance between the modes of the beam and string, principal parametric resonance for the beam, and primary resonance for the string is considered. The method of multiple scales is utilized to analyze the nonlinear responses of the string-beam coupled system. Based on the averaged equation obtained here, the techniques of phase portrait, waveform, and Poincare map are applied to analyze the periodic and chaotic motions. It is found from numerical simulations that there are obvious jumping phenomena in the resonant response–frequency curves. It is indicated from the phase portrait and Poincare map that period-4, period-2, and periodic solutions and chaotic motions occur in the transverse nonlinear vibrations of the string-beam coupled system under certain conditions. An erratum to this article is available at .     

Variational solutions for some steady and non-steady laminar viscous flows with stagnation points

Recently, Lebon and Lambermont proposed a general variational principle for fluid mechanics. In this paper, the criterion is applied to steady and non-steady stagnation flows; the plane and the axisymmetrical cases are considered. By using Glansdorff-Prigogine self consistent method, approximate analytic solutions are derived. It is shown that the steady solution is rather quickly reached. For this latter case, the present solutions are compared with previous ones obtained by direct integration of the Navier-Stokes equations.     

On the nonlinear mechanics of discrete networks

Summary A formulation of the equilibrium problem for nonlinear elastic networks is presented. Explicit necessary and sufficient conditions for minimum-energy configurations are derived. These are used to generate a relaxed formulation of the theory in which fibre slackening is accounted for automatically. For the relaxed problem, minimum-energy and uniqueness theorems are proved and used as the basis of a numerical method in which equilibrium configurations are recovered asymptotically in the long-time limit of an artificial dynamical problem. Such an approach is particularly useful for networks, as stiffness-based equilibrium formulations are known to suffer from ill-conditioning in a wide variety of applications. Several illustrative examples are discussed. Accepted for publication 22 June 1996     

„Fouling“-Vorgänge bei der Verdampfung von Argon im waagerecht durchströmten Rohr

Zusammenfassung Bei Messungen des Wärmeübergangs beim Strömungssieden von Argon wurde ein zeitlicher Anstieg der Wandtemperatur beobachtet, während die Einstellparameter Wärmestromdichte, Massenstromdichte, Dampfgehalt und Systemdruck konstant blieben. Dieser Temperaturanstieg endete nach mehreren Stunden bei einer beträchtlich höheren Wandtemperatur oder mit dem Eintreten der Siedekrise. Als Ursache für dieses Phänomen wurde die Ablagerung von im Argon gelöstem CO₂ an der Heizfläche ermittelt, wobei zu beachten ist, daß die Reinheit des verwendeten Argons größer als 99,996 vol-% war. In weiteren Versuchen wurde der Einfluß der CO₂-Konzentration auf diesen Fouling-Vorgang bestimmt und ein Verfahren entwickelt, um das CO₂ aus dem Meßkreislauf zu entfernen. Der Ablagerungsmechanimus und der Einfluß der Betriebsparameter auf die Ablagerungsgeschwindigkeit können mit Modellvorstellungen zur Blasenbildung erklärt werden.

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Fouling-phenomena during the evaporation of argon within a horizontal tube

During heat transfer measurements at flow boiling of argon a transient increase of the wall temperature has been observed, though the parameters such as heat flux, mass velocity, flow quality and system pressure were kept constant. This temperature drifting ended after several hours at a considerably higher wall temperature or with the boiling crisis. Although the purity of the test substance was higher than 99.996 vol-%, this phenomenon was caused by the solidification of CO₂ on the heating surface. Further investigations showed the influence of the CO₂-concentration on the drifting as well as a method to remove the CO₂ out of the test fluid. Both, fouling mechanism and influence of the parameters on the fouling, can be explained satisfactorily by means of bubble-growth mechanisms.

     

Universal solutions for fiber-reinforced compressible isotropic elastic materials

Universal solutions for fiber-reinforced compressible isotropic elastic materials under large elastic deformations are obtained, by using inverse methods.The following deformations are investigated: bending, stretching and shearing of a rectangular block; straightening, stretching and shearing of a sector of a circular tube; inflation, eversion, extension, torsion, bending and shearing of a sector of a circular tube; inflation and eversion of a spherical shell.The significance of the reinforcement and the deformed configuration of the fibers is duscussed.

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Zusammenfassung Unter Benützung inverser Methoden werden universelle Lösungen für faser-vorgespanntes, Kompressibles, isotropes, elastisches Material angegeben.Die folgenden Deformationen werden untersucht: Biegung, Zug und Schub eines rechteckigen Blockes; Ausgradung, Zug und Schub eines Sektors eines Kreisrohrausschnitts; isotrope Dehnung, Umstülpung, Erweiterung, Tordierung, Biegung und Schub eines Sektors eines Kreisrohres; isotrope Dehnung und Umstülpung einer Kugelschale.Die Bedeutung der Vorspannung und der verformten Konfiguration der Fasern wird diskutiert.

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Graduate Student.