The transverse motion of a translating tensioned Euler-Bernoulli beam is controlled by passive or active damping applied at a boundary. Even for an undamped beam with a symmetric boundary configuration, the interaction between the translating continuum and the stationary or moving boundary leads to energy variation in free motion. With the time-varying energy chosen as a Lyapunov functional, boundary control laws are designed based on Lyapunov’s second method. For various types of translating beams, energy dissipation by boundary damping is quantified using the method of traveling waves. The optimal value of damping, maximizing the energy dissipation, is also explicitly represented by system parameters. The analytical results are compared with numerical simulations using the finite difference scheme.

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