Exact frequency response of bars with multiple dampers

The paper addresses the frequency analysis of bars with an arbitrary number of dampers, subjected to harmonically varying loads. Multiple external/internal dampers occurring at the same position along the bar, modelling external damping devices and internal damping due to damage or imperfect connections, are considered. In this context, the challenge is to handle simultaneous discontinuities of the response variables, i.e. axial force/displacement discontinuities at the location of external/internal dampers. Based on the theory of generalized functions, the paper will present exact closed-form expressions of the frequency response under point/polynomial loads, which hold regardless of the number of dampers. In addition, closed-form expressions will be derived for the exact dynamic stiffness matrix and load vector of the bar, to be used in a standard assemblage procedure for an exact frequency response analysis of 2D truss structures. Changes to consider a single damper at a given position are straightforward. Numerical applications show the advantages of the proposed method.