A review of development and implementation of an active nonlinear vibration absorber

We present an account of an implementation of an active nonlinear vibration absorber that we have developed. The control technique exploits the satura tion phenomenon that is known to occur in quadratically-coupled multi-degre e-of-freedom systems subjected to primary excitation and possessing a two-t o-one internal resonance. The technique is based on introducing an absorber and coupling it with the structure through a sensor and an actuator, where the feedback and control signals are quadratic. First, we consider the cas e of controlling the vibrations of a single-degree-of-freedom system. We de velop the equations governing the response of the closed-loop system and us e the method of multiple scales to obtain an approximate solution. We inves tigate the performance of the control strategy by studying its steady-state and transient characteristics. Additionally, we compare the performance of the quadratic absorber with that of a linear absorber. Then, we present th eoretical and experimental results that demonstrate the versatility of the technique. We design an electronic circuit to emulate the absorber and use a variety of sensors and actuators to implement the active control strategy . First, we use a motor and a potentiometer to control the vibration of a r igid beam. We develop a plant model that includes Coulomb friction and demo nstrate that the closed-loop system exhibits the saturation phenomenon. Sec ond, we extend the strategy to multi-degree-of-freedom systems. We use PZT ceramics and strain gages to suppress vibrations of flexible steel beams wh en subjected to single- and simultaneous two-mode excitations. Third, we em ploy Terfenol-D, a nonlinear actuator, and accelerometers to control the vi brations of flexible beams. In all instances, the technique is successful i n reducing the response amplitude of the structures.