Frequency-domain mathematical model of the smart spring device for vibration reduction

In this paper, the capability of a semi-active device for vibration control, named Smart Spring, is analytically investigated. Such a device allows to actively control vibration by modulating the structural properties, such as the mass, stiffness, or damping, of a system, through a piezoceramic actuator. The analytical study of the Smart Spring is performed by developing its mathematical model in the frequency domain, in order to evaluate the response of the system in terms of its harmonic components. Furthermore, an open-loop control law for the modulation of the system stiffness is introduced. It is shown that the displacement solution depends on three dimensionless parameters, representing both structural and control properties of the system, that can be opportunely chosen to reduce the response, then vibration.