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.