Positioning and tuning of viscous damper on flexible structure

The complex eigenvalues of a flexible structure including a viscous damper are derived by solving the root locus of a transfer function that is composed of very easily identifiable parameters: the static stiffness of the structure at the damper location, the resonance frequencies of the undamped structure and the resonance frequencies of the structure in which the damper is replaced by a rigid link. Approximate solutions are proposed for the complex eigenvalues and formulas are derived for the maximum modal damping ratio and the optimal damping constant. The correctness of the formulas is illustrated by numerical examples of a cantilever beam with attached viscous damper. Although approximate solutions exist which are not restricted to the case of a single damper, these are only accurate when the difference between the undamped and constrained eigensolution is sufficiently small, while the approximations obtained in the present paper are accurate in a broader range without losing simplicity.