Suppressing self-excited vibrations by synchronous and time-periodic stiffness and damping variation

Stability investigations on vibration suppression employing the concept of actuators with variable stiffness and damping elements are presented. Systems with two and more degrees of freedom with linear spring- and damping-elements are considered, that are subject to self-excitation as well as parametric excitation by simultaneous stiffness and damping variation. General conditions for full vibration suppression are derived analytically by applying a singular perturbation method of first order. 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. The results are compared to former investigations of systems with a pure stiffness variation and a pure damping variation in time. While a specific parametric stiffness or damping excitation may suppress the system vibrations successfully, the interaction of both excitations modifies the formerly gained stability regions in the system parameter space. The analytical predictions are verified for exemplary systems by exact numerical time integration. These basic results obtained can be used for design of a control strategy for actuators with synchronously variable stiffness and damping elements to suppress transient vibrations. (c) 2007 Elsevier Ltd. All rights reserved.