Closed-loop control of the smart spring. An analytical solution for the actuator model

The analytical modeling of the Smart Spring actuator for vibration reduction of periodically excited systems is performed. The mathematical model is developed in the frequency domain using the harmonic balance method, assuming that the solution is harmonic on the exciting frequency. Both the fixed-base and base-excited configurations are studied. It is shown that the Smart Spring transmissibility at the target frequency depends on only three dimensionless parameters associated with the stiffness modulation characteristics of the device for the fixed-base configuration and five dimensionless parameters for the base-excited configuration. The fundamental values for the Smart Spring closed-loop control are discussed.