Wave characteristics and vibration control of translating beams by optimalboundary damping

The transverse motion of a translating tensioned Euler-Bernoulli beam is co ntrolled by passive or active damping applied at a boundary. Even for an un damped beam with a symmetric boundary configuration, the interaction betwee n the translating continuum and the stationary or moving boundary leads to energy variation in free motion. With the time-varying energy chosen as a L yapunov functional, boundary control laws are designed based on Lyapunov's second method. For various types of translating beams, energy dissipation b y boundary damping is quantified using the method of traveling waves. The o ptimal value of damping, maximizing the energy dissipation, is also explici tly represented by system parameters. The analytical results are compared w ith numerical simulations using the finite difference scheme.