Damping by Parametric Stiffness Excitation: Resonance and Anti-Resonance

Abstract

Investigations are presented into the stability of vibration suppression employing variable-stiffness actuators. Systems with an arbitrary number of degrees of freedom are considered, and are subject to both parametric excitation and self-excitation. Analytical conditions of stability and instability are derived by applying a singular perturbation technique. These conditions enable a stability classification that naturally leads to the description parametric anti-resonance. The influence of the symmetry property of the parametric excitation matrix on the location of the parametric anti-resonance is discussed. Additionally, the influence of parametric resonance and anti-resonance on the eigenvalues corresponding to the slow motion of a generic system are analysed. A geometric interpretation is presented, enabling deeper insight into the mechanism of vibration suppression, and leading to the interpretation of coupling modes using parametric anti-resonance and amplification of system damping. The basic results obtained can be used for design of a control strategy for variable-stiffness actuators.