Active Vibration Control of a Flexible Beam Using a Buckling-Type End Force

In this paper, we explore the use of end forces for vibration control in structural elements. The process involves vibration measurement and observer-based estimation of modal amplitudes, which are used to determine when to apply an end load such that it will remove vibration energy from the structure. For this study, we consider transverse vibration of a cantilever beam with a buckling-type end load that can be switched between two values, both of which are below the buckling load. The stability of the control system is proven using Lyapunov stability theory and its effectiveness is demonstrated using simulations and physical experiments. It is shown that the effectiveness of the approach is affected by the bandwidth of the actuator and the attendant characteristics of the filter, the level of the control force, and the level of bias in the end force. The experiments employ a beam fitted with a cable mechanism and motor for applying the end force, and a piezoelectric patch for taking vibration measurements. It is shown that the first two modes of the beam, whose natural frequencies are less than the bandwidth of the motor, are very effectively controlled by the proposed scheme.