Vibrations of a taut cable with an external damper

A solution is presented of the problem of vibrations of a taut cable equipped with a concentrated viscous damper. The solution is expressed in terms of damped complex valued modes, leaning to a transcendental equation for the complex eigenfrequencies. A simple iterative solution of the frequency equation for all complex eigenfrequencies is proposed. The damping ratio of the vibration modes, determined from the argument of the complex eigenfrequency are typically determined to within one percent in two iterations. An accurate asymptotic approximation of the damping ratio of the lower modes is obtained. This formula permits explicit determination of the optimal location of the viscous damper, depending on its damping parameter.