Vibration of Tensioned Beams With Intermediate Damper. I: Formulation, Influence of Damper Location
Joseph A. Main, Nicholas P. Jones
Exact analytical solutions are formulated for the complex eigenmodes of tensioned beams with an intermediate viscous damper. The problem is formulated using the dynamic stiffness method, and characteristic equations are obtained for both clamped and pinned supports. The complex eigenfrequencies form loci in the complex plane that originate at the undamped eigenfrequencies and terminate at the eigenfrequencies of the fully locked system, in which the damper acts as an intermediate pin support. The fully locked eigenfrequencies exhibit curve veering , in which adjacent eigenfrequencies approach and then veer apart as the damper passes a node of an undamped mode shape. Consideration of the evolution of the eigenfrequency loci with varying damper location reveals three distinct regimes of behavior, which prevail from the taut-string limit to the case of a beam without tension. The second regime corresponds to damper locations near the first anti-node of a given undamped mode shape; in this regime the loci bend backwards to intersect the imaginary axis, and two distinct non-oscillatory decaying solutions emerge when the damper coefficient exceeds a critical value.
and Jones, N.
Vibration of Tensioned Beams With Intermediate Damper. I: Formulation, Influence of Damper Location, Journal of Engineering Mechanics-Asce, [online], https://doi.org/10.1061/(ASCE)0733-9399(2007)133:4(369)
(Accessed February 21, 2024)