Modal control of vibration in rotating machines and other generally damped systems

Second-order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual off-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper, a method to utilise modal control using the decoupled second-order matrix equations involving non-classical damping is proposed. An example of modal control successfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components.