Vibration of Tensioned Beams with Intermediate Damper. II: Damper Near Support
Joseph A. Main, Nicholas P. Jones
Exact analytical solutions are used to investigate the complex eigenfrequencies of tensioned beams with a viscous damper attached transversely near a support, for which the complex eigenfrequencies remain fairly close to their undamped values. This problem is of particular relevance for stay-cable vibration suppression, but no restrictions on the 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 can be accurately computed within a few iterations. Explicit asymptotic approximations for the complex eigenfrequencies are also obtained, subject to further restrictions on the closeness of the eigenfrequencies to their undamped values. These asymptotic approximations are expressed in the same universal form previously identified for the taut string with intermediate damper, but the maximum attainable modal damping ratios and the corresponding optimal damper tuning can be significantly affected by bending stiffness and by the nature of the support conditions.
and Jones, N.
Vibration of Tensioned Beams with Intermediate Damper. II: Damper Near Support, Journal of Engineering Mechanics-Asce, [online], https://doi.org/10.1061/(ASCE)0733-9399(2007)133:4(379)
(Accessed June 10, 2023)