A linearized analysis for frictionally damped systems

Abstract A system comprising a linear, undamped, multi-degree of freedom structure with a single frictional damper linking two coordinates and excited by any number of arbitrarily located sinusoidal applied forces is considered. A linearized method of analysis is developed giving analytical expressions for the general response of the system for both slip and no-slip conditions at the damper interface. The theory is compared with the linearized formulation given by Den Hartog [1956 Mechanical Vibrations , McGraw-Hill] and with experimental measurement. It is shown that the inclusion of a linear dependence on the relative slip amplitude in the expression for the frictional force during slipping produces a significant improvement in the response prediction capability of the theory over Den Hartog's method. The results presented show good agreement between the predicted and experimentally measured responses.