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The total mechanical energy associated with an axially moving string or beam that travels between two supports is not constant. In general, the total energy varies at twice the frequency of free oscillations. The time-dependent component of the energy derives from energy flux through the supports, and the convective velocity of material particles in the continuum renders the net flux nonzero. Expressions for the temporal variation of the energy associated with the string and beam models are derived and analyzed. For single-mode free response of the traveling string, the total energy is constant at particular transport speeds.
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Wickert et al. (1989) studied this question.
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