Active nonlinear inerter damper for vibration mitigation of Duffing oscillators

In this paper, a nonlinear active damping strategy based on force feedback is proposed. The proposed device is composed of a pair of collocated actuator and force sensor. The control law is formed by feeding back the output of the force sensor, through one single, one double integrator and another double integrator of its cube. An equivalent mechanical network which consists of a dashpot, an inerter and a cube root inerter is developed to enable a straightforward interpretation of the physics behind. Closed-form expressions for the optimal feedback gains are derived. Numerical validations are performed to demonstrate the proposed control strategy.