Drill strings are slender structures used extensively in drilling and mining operations. In this thesis work, secondary-frequency input additions to the drive speed input are considered and the resulting influence on system dynamics is examined. Experimental studies are conducted with a laboratory scale drill-string arrangement, and high-frequency and low-frequency additions are considered for cases in which the drive speed frequency is close to either a bending mode or torsion mode natural frequency. It is found that carefully chosen secondary-frequency additions can be used to attenuate undesirable system dynamics, especially, for rotary systems. To complement the experiments, numerical studies are conducted with a reduced-order model of the drill-string system. The obtained numerical results are found to be in reasonable agreement with the experimental results. Preliminary numerical results obtained in the presence of rotor-stator interactions are also included. In addition, areas in which the model construction will need further development are also discussed. The findings of this work can be useful for considering secondary-frequency addition based schemes for controlling bending and torsional motions of drill-string systems.