Complex Modal Analysis of a Taut Cable with Three-Element Maxwell Damper

Free vibrations of a taut cable with an attached three-element Maxwell damper were investigated by using an analytical formulation of the complex eigenvalue problem.As the viscous damper,its inherent stiffness and supporter were represented as a three-element Maxwell model,the equations of motion of the cable and the three-element Maxwell damper system were obtained.The damping properties in the free vibration of the system were extracted by complex-mode analysis technique.An explicit analytical approximation was obtained,when the damper was installed near the cable anchorage.The full solution was evaluated numerically by iteration,and the results showed that the approximate explicit formulae were rather accurate.This study shows that the interaction between the inherent stiffness of the damper and the flexibility of the supporter in the viscous damper reduces the damper effectiveness.The optimum damping coefficient of the three-element Maxwell damper increases when the inherent stiffness of the damper increases,but decreases when the flexibility of the supporter increases.