Application of a passive/active autoparametric cantilever beam absorber with PZT actuator for Duffing systems

An experimental investigation is carried out on a cantilever-type passive/active autoparametric vibration absor-ber, with a PZT patch actuator, to be used in a primary damped Duffing system. The primary system consists of a mass, viscous damping and a cubic stiffness provided by a soft helical spring, over which is mounted a cantilever beam with a PZT patch actuator actively controlled to attenuate harmonic and resonant excitation forces. With the PZT actuator on the cantilever beam absorber, cemented to the base of the beam, the auto-parametric vibration absorber is made active, thus enabling the possibility to control the effective stiffness and damping associated to the passive absorber and, as a consequence, the implementation of an active vibration control scheme able to preserve, as possible, the autoparametric interaction as well as to compensate varying excitation frequencies and parametric uncertainty. This active vibration absorber employs feedback information from a high resolution optical encoder on the primary Duffing system and an accelerometer on the tip beam absorber, a strain gage on the base of the beam, feedforward information from the excitation force and on-line computations from the nonlinear approximate frequency response, parameterized in terms of a proportional gain provided by a voltage input to the PZT actuator, thus modifying the closed-loop dynamic stiffness and providing a mechanism to asymptotically track an optimal, robust and stable attenuation solution on the primary Du-ffing system. Experimental results are included to describe the dynamic and robust performance of the overall closed-loop system