Simple viscoelastic dampers have been invented for use on the root attachments of turbomachine blades. These dampers suppress bending- and torsion-mode blade vibrations, which are excited by unsteady aerodynamic forces during operation. In suppressing vibrations, these dampers reduce fatigue (thereby prolonging blade lifetimes) while reducing noise. These dampers can be installed in new turbomachines or in previously constructed turbomachines, without need for structural modifications. Moreover, because these dampers are not exposed to flows, they do not affect the aerodynamic performances of turbomachines.