Vibration of Tensioned Beams with Intermediate Damper. II: Damper near a Support

Abstract

Analytical solutions are used to investigate the free vibrations of tensioned beams with a viscous damper attached transversely near a support. This problem is of particular relevance for stay-cable vibration suppression, but no restrictions on the level of axial load are introduced, and the results are quite broadly applicable. Characteristic equations for both clamped and pinned supports are rearranged into forms suitable for numerical solution by fixed-point iteration, whereby the complex eigenfrequencies and corresponding damping ratios can be accurately computed within a few iterations. Explicit asymptotic approximations for the complex eigenfrequencies are also obtained, subject to restrictions on the closeness of the eigenfrequencies to their undamped values. These asymptotic approximations are expressed in the same “universal” form identified in previous studies. It is observed that the maximum attainable modal damping ratios and the corresponding optimal values of the damper coefficient can be significantly affected by bending stiffness and by the nature of the support conditions, and a nondimensional parameter grouping is identified that enables an assessment of when bending stiffness should be considered.