Search

Torsional vibrations in beams are damped by discrete, axial viscous dampers in configurations constituting bimoments. The bimoments act on warping displacements and partial restraining of warping suggests the inclusion of a flexibility parameter, calibrated from numerical results. Correcting for distortion is incorporated in a similar manner. The use of the governing differential equation with calibrated parameters as an alternative to a full complex analysis by a FE model is justified by an example. It is demonstrated that the differential equation determines the damped frequencies and damping ratios with great accuracy. Significant damping ratios of the lowest torsional mode are obtained.

For damping of fully coupled beam vibrations, a three-component tuned mass absorber is proposed, consisting of two translational and a single-rotational absorber, which together target a specific vibration mode. The representation of the interaction with residual nonresonant vibration modes is consistently included by two supplemental terms in the absorber equation, calibrated by frequency matching with the full structural model for vanishing absorber damping. The absorber tuning directly includes these residual terms without approximation when the underlying modal representation is based on the vibration form with absorber masses rigidly attached to the structure. It is demonstrated that the desired damping behavior requires nonhomogeneous absorber balancing, obtained by an approximate method for the relative sizing of each absorber mass.

This paper considers damping of torsional beam vibrations by active control of the axial warping displacements. A beam element with active positive position feedback (PPF) is set up with an additional flexibility parameter. This arises from partial restraining of warping caused by discrete actuators. The flexibility lowers the frequency associated with an infinite actuator gain and thereby the attainable damping ratio. It is shown how it furthermore affects the stability limit. Results are compared with three-dimensional finite element results, with multiple actuators acting on an end cross-section of the beam. The accuracy of the beam model is justified by an example which shows that substantial damping ratios may be achieved by active warping control.

Damping of torsional beam vibrations of slender beam–structures with thin–walled cross–sections is investigated. Analytical results from solving the differential equation governing torsion with viscous bimoments imposed at the boundary, are compared with a numerical approach with three–dimensional, is oparametric elements. The viscous bimoments act on the axial warping displacements associated with in homogeneous torsion, and are in a numerical format realized by suitable configurations of concentrated, axial forces describing discrete dampers.It is illustrated by an example that significant damping ratios may be obtained for a beam withan open cross–section.

Supplemental damping of torsional beam vibrations is considered by viscous bimoments acting on the axial warping displacement at the beam supports. The concept is illustrated by solving the governing eigenvalue problem for various support configurations with the applied bimoments represented as viscous boundary conditions. It is demonstrated that properly calibrated viscous bimoments introduce a significant level of supplemental damping to the targeted vibration mode and that the attainable damping can be accurately estimated from the two undamped problems associated with vanishing and infinite viscous parameters, respectively.