Summary
The paper deals with an analysis of different models of continuous systems subjected to a load distributed over a given length and moving at a constant velocity.
The general discussion concerns a beam resting on a viscoelastic semi-space. The motion of the body is described by polynomial differential operators. With body forces being disregarded, the motion of the beam lying on a viscoelastic foundation is discussed with either taking into account the effect of shear deflection and the inertia of rotation or with neglecting them. Consideration is also given to the cases of relative motion of two continuous systems and the stability of their interaction. The above cases represent the models of a number of mechanical systems applied in e.g. modern transportation facilities, technology of bonding of layer materials, etc.
The analysis is substantially simplified because the equations of motion and the boundary conditions are written in a moving coordinate system related with the load and only stationary solutions are considered. With such an approach, the solutions depend only on the transformed space variable, while the velocity of the load appears as one of the parameters of the system. Interesting conclusions are drawn from the obtained solutions and numerical calculations.
Übersicht
Der vorliegende Beitrag behandelt die Analyse von kontinuierlichen Systemen, die verteilten bewegten Lasten ausgesetzt sind. Es wird zunächst ein Balken auf viskoelastischem Halbraum behandelt. Die Bewegung des Körpers wird beschrieben durch Differentialoperatoren in Polynomform, wobei der Einfluß von Schubverformung und Drehträgheit diskutiert wird. Der Fall der Relativbewegung von zwei kontinuierlichen Systemen und ihre Stabilität wird ebenfalls diskutiert. Die untersuchten Fälle stellen Modelle zahlreicher mechanischer Systeme dar, wie zum Beispiel moderne Schnelltransportsysteme, Fügevorrichtungen von Schichtmaterialien, usw.
Die Analyse der Probleme wird wesentlich dadurch vereinfacht, daß die Bewegungsgleichungen und Randbedingungen in einem mitbewegten Koordinatensystem formuliert werden und nur stationäre Lösungen betrachtet werden. Auf diese Weise hängen die Lösungen nur von der transformierten Ortsvariablen ab; die Geschwindigkeit der Belastung tritt als ein Parameter des Systems auf.
Aufschlußreiche Schlußfolgerungen werden anhand der erhaltenen Lösungen und numerischen Berechnungen dargestellt.
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Bogacz, R. On dynamics and stability of continuous systems subjected to a distributed moving load. Ing. arch 53, 243–255 (1983). https://doi.org/10.1007/BF00532244
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DOI: https://doi.org/10.1007/BF00532244