The investigational results for an active vibration control of a translating tensioned beam with a varying traveling speed are presented. The dynamics of beam and actuator is modeled via the extended Hamilton's principle. In a proper mathematical manner, the Lyapunov method is employed to design a boundary control law for ensuring the vibration reduction of the nonlinear time-varying system and also to ensure the exponential stability of the closed-loop system.
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Yang et al. (2005) studied this question.
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