A design procedure for active control of beam vibrations

The transverse vibrations of beams is discussed and a methodology for the design of an active damping device is given. The Bernoulli-Euler equation is used to derive a transcendental transfer function, which relates a torque applied at one end of the beam to the rotational position and velocity at that point. The active damping device consists of a wire, a linear actuator and a short torque arm attached to one end of the beam. The action of the actuator varies a tension in the wire and creates a torque which opposes the rotation of the beam and thus damps vibration. A design procedure for such an active damper is given. This procedure shows the relationships and trade-offs between the actuator stroke, power required, stress levels in the wire and beam and the geometry of the beam and wire. It is shown that by consideration of the frequency response at the beam natural frequencies, the aforementioned relationships can be greatly simplified. Similarly, a simple way of estimating the effective damping ratios and eigenvalue locations of actively controlled beams is presented.