Damping of coupled bending-torsion beam vibrations by a two-dof tmd with analogous coupling

Coupled bending-torsion vibrations of a beam with a single cross-section axis of symmetry are mitigated by a two-degree-of-freedom (dof) tuned mass damper with a coupling analogous to that of the beam. By modal truncation a four-degree-of-freedom model is derived for tmd tuning. Because of the analogous tmd properties, a stiffness tuning formula identical to that for the classic tuned mass damper secures inverse relations between all four undamped natural frequencies. Expressions for the tmd damping are subsequently found by a numerical search, which maximizes the smallest of the four damping ratios, resulting in equal damping in three of the four modes. The two-dof coupled tmd is finally assessed by numerical root locus and frequency response analysis for a full flexible beam.