The effect of vibration localization on the performance of a viscous damper

The presence of irregularity in a periodic structure results in the vibration localization which exhibits locally large amplitude. The combination of the vibration localization and a viscous damper can be one way to realize a fast damping of free vibration by intentionally creating a vibration mode which is strongly localized at the damper position. This paper investigates the behaviour of a uniform tensioned string which is coupled to ground through homogeneously distributed stiffness and to a viscous damper at its centre, examining the effect of vibration localization on the damping performance. Localization is induced by a concentrated mass that is attached to the string at the same point as the viscous damper. In order to evaluate the rate of vibration decay, the characteristic equation is derived and the eigenvalue is computed by the Galerkin Method in which the mode of the string is represented by the superposition of a half sine wave and shape functions whose slope is discontinuous at the position of the added mass. The results show that the added concentrated mass induces vibration mode which is strongly localized at the damper position, demonstrating improvement in damping performance with the increasing concentrated mass.