Averaging in vibration suppression by parametric stiffness excitation

Stability investigations of vibration suppression employing the concept of actuators with a variable stiffness 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 stiffness excitation. General conditions for full vibration suppression and conditions of instability are derived analytically by applying a singular perturbation of first and second order. The analytical predictions are compared for exemplary systems by numerical time integration and show a great improvement of former results. These basic results obtained can be used for accurate design of a control strategy for actuators.