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Title of Journal: Acta Mech Sin

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Abbravation: Acta Mechanica Sinica

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Springer-Verlag

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DOI

10.1016/j.actamat.2006.02.014

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1614-3116

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Energetics and conserved quantity of an axially mo

Authors: Liqun Chen C W Lim Hu Ding
Publish Date: 2007/11/07
Volume: 24, Issue: 2, Pages: 215-221
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Abstract

Nonlinear threedimensional vibration of axially moving strings is investigated in the view of energetics The governing equation is derived from the Eulerian equation of motion of a continuum for axially accelerating strings The timerate of the total mechanical energy associated with the vibration is calculated for the string with its ends moving in a prescribed way For a string moving in a constant axial speed and constrained by two fixed ends a conserved quantity is proved to remain unchanged during threedimensional vibration while the string energy is not conserved An approximate conserved quantity is derived from the conserved quantity in the neighborhood of the straight equilibrium configuration The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equilibrium configuration Numerical simulations are performed for a rubber string and a steel string The results demonstrate the variation of the total mechanical energy and the invariance of the conserved quantityThe project supported by the National Natural Science Foundation of China 10472060 Research Grants Council of the Hong Kong Special Administrative Region 9041145 Shanghai Municipal Education Commission Scientific Research Project 07ZZ07 and Shanghai Leading Academic Discipline Project Y0103

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