| The steady-state response to periodic excitation of multi-degree of freedom (DOF) structural systems with several elastic/perfectly plastic attached dry friction dampers is studied. The force transmitted by a friction damper is deduced in the time domain from the displacement and velocity of the corresponding DOF to which the friction damper is attached. The convergence of the method is ensured by a modified Broyden's algorithm, which is used to solve iteratively the set of multi-harmonic nonlinear equations in the frequency domain. The solution algorithm is thus hybrid in the frequency and time domains. The method proposed can handle both friction dampers that are attached to ground and the general case of dampers that connect two DOF's of the structure. Results are obtained for both tuned and mistuned configurations of large-scale models of dry-friction damped bladed disks used in turbomachinery applications, subject to various traveling wave “engine order” excitations, for a variety of structural and friction parameters. Interesting, complex features of the nonlinear response are revealed, such as: motions for several stick-slip phases per period; localized motions for mistuned systems, which feature mostly sticking motion at most blades and mostly slipping motion at a few blades; subresonances; effects of higher harmonics. Free response and stability analyses are also presented for structural systems attached to a single friction damper. Finally, a novel, general model of friction damper is introduced: the damper element is a general, massless structure connected at multiple punctual interfaces to the adjacent structures. This model allows for a rich combination of stick/slip dynamic motion at the various interfaces. It is believed to provide an accurate behavior of dry friction-damped blade assemblies. |
