International Conference on Engineering Vibration, Sofia, Bulgaria, International Conference on Engineering Vibration 2017

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DISSIPATIVE PROPERTIES OF THE END REACTIVE LOADS
Alexander Sergeyev

Last modified: 2017-05-20

Abstract


The dynamics of pipes, conveying heavy fluid is under consideration. We reproduce the derivation of the differential equation of motion for a rectilinear rigid pipe with a heavy fluid by use of the canonical procedure, based on the d’Alembert Principle. Then we do the same by means of the Fundamental Laws of the Euler dynamics for open systems. The result allows to give the alternative physical sense for the damping load in such a system. It turned the damping is connected with the reactive loads at the end of the pipe. The conclusion has been verified for a semisecular pipe, conveying heavy fluid. It is the <>—like system. The literal derivation of the equation of motion for this system by means of the d’Alembert Principle, leads to the absurd result: the equation of motion predicts, that the free <>-like system has not a stationary rotation as a solution. That result proves that the d'Alembert Principle cannot be used as a reliable instrument to the mathematical simulating of the open systems dynamics.

However we have obtained the differential equation of motion for the Segner Wheel by means of the Fundamental Laws of the Euler dynamics for open systems. This approach gives the equation, which has a non contradictory physical interpretation for each term, and predictions of the equation are really observed. This result allows to confirm the explanation to the nature of damping in such a system. The damping does not depend on the Coriolis forces as it is considered in the classical works on the pipeline dynamics. In reality this phenomena is produced by the end reactive loads.
On the base of the obtained results it is presented the possible explanation for the so called Paidoussis paradox of non monotonicity, known in the literature on the pipeline dynamics since 1966.