Component mode analysis of a simple non-linear,non-conservative system

A component mode analysis is carried out based upon the use of constraint conditions and Lagrange multipliers to treat exemplary physical systems with non-linear damping. Both viscous and dry friction dampers attached to a linear elastic (beam) system are examined. The method is shown to possess conceptual and computational advantages by its ability to reduce the analysis of a multimode system to a small number of degrees of freedom equal to that associated with the non-linear component.