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Generally, a mechanical system always has symmetric system matrices. Nevertheless, when some non-conservative forces are included, such as friction and aerodynamic force, the symmetry of the stiffness matrix or damping matrix or both violated. Moreover, such an asymmetric system is prone to dynamic instability. Distinct from the eigenvalue assignment for symmetric systems to reassign their natural frequencies, the main purpose of eigenvalue assignment for asymmetric systems is to shift the unstable eigenvalues to the stable region. In this research, only the unstable eigenvalues and eigenvalues which are close to the imaginary axis of the complex eigenvalue plane are assigned due to their predominant influence on the response of the system. The remaining eigenvalues remain unchanged. The state-feedback control gains are obtained by solving the constrained linear least-squares problems in which the linear system matrices are deduced based on the receptance method and the constraint is derived from the unobservability condition. The numerical simulation results demonstrate that the proposed method is capable of partially assigning those targeted eigenvalues of the system for stabilisation.

Active partial eigenvalue assignment for friction-induced vibration using receptance method