General parametric stiffness excitation - anti-resonance frequency and symmetry

Stability investigations on vibration cancelling employing the concept of actuators with general stiffness elements are presented. Systems with an arbitrary number of degrees of freedom with linear spring- and damping elements are considered, that are subject to self-excitation as well as parametric excitation by stiffness variations with arbitrary phase relations. General conditions for full vibration suppression are derived analytically by applying a singular perturbation technique. These conditions naturally lead to the terms of parametric resonance and anti-resonance and enable a stability classification with respect to the parametric excitation matrices and their symmetry properties. The results are compared to former investigations of systems with a single or synchronous stiffness variation in time and geometrical interpretations are given. These basic results obtained can be used for design of a control strategy for actuators with periodically actuated stiffness elements and arbitrary phase relations.