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

Summary We present an account of an implementation of an active nonlinear vibration absorber that we have developed. The control technique exploits the saturation phenomenon that is known to occur in quadratically-coupled multi-degree-of-freedom systems subjected to primary excitation and possessing a two-to-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 case of controlling the vibrations of a single-degree-of-freedom system. We develop the equations governing the response of the closed-loop system and use the method of multiple scales to obtain an approximate solution. We investigate 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 theoretical 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 rigid beam. We develop a plant model that includes Coulomb friction and demonstrate that the closed-loop system exhibits the saturation phenomenon. Second, we extend the strategy to multi-degree-of-freedom systems. We use PZT ceramics and strain gages to suppress vibrations of flexible steel beams when subjected to single- and simultaneous two-mode excitations. Third, we employ Terfenol-D, a nonlinear actuator, and accelerometers to control the vibrations of flexible beams. In all instances, the technique is successful in reducing the response amplitude of the structures.