The Rate of Change of an Energy Functional for Axially Moving Continua

  • Yang, Kyung-Jinn (Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications) ;
  • Hong, Keum-Shik (School of Mechanical Engineering, Pusan National University) ;
  • Matsuno, Fumitoshi (Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications)
  • Published : 2003.10.22

Abstract

In this paper, with the utilization of a three-dimensional version of Leibniz’s rule, the procedure of deriving the time rate of change of an energy functional for axially moving continua is investigated. It will be shown that the method in [14], which describes the way of getting the time rate of change of an energy functional in Eulerian description, and subsequent results in [10, 11] are not complete. The key point is that the time derivatives at boundaries in the Eulerian description of axially moving continua should take into account the velocity of the moving material itself. A noble way of deriving the time rate of change of the energy functional is proposed. The correctness of the proposed method has been confirmed by other approaches. Two examples, one-dimensional axially moving string and beam equations, are provided for the purpose of demonstration. The results following the procedure proposed and the results in [14] are compared.

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