  This work addresses friction-induced modal interactions in jointed
structures, and their effects on the passive mitigation of vibrations by means
of friction damping. Under the condition of (nearly) commensurable natural
frequencies, the nonlinear character of friction can cause so-called nonlinear
modal interactions. If harmonic forcing near the natural frequency of a
specific mode is applied, for instance, another mode may be excited due to
nonlinear energy transfer and thus contribute considerably to the vibration
response. We investigate how this phenomenon affects the performance of
friction damping. To this end, we study the steady-state, periodic forced
vibrations of a system of two beams connected via a local mechanical friction
joint. The system can be tuned to continuously adjust the ratio between the
first two natural frequencies in the range around the $1:3$ internal resonance,
in order to trigger or suppress the emergence of modal interactions. Due to the
re-distribution of the vibration energy, the vibration level can in fact be
reduced in certain situations. However, in other situations, the multi-harmonic
character of the vibration has detrimental effects on the effective damping
provided by the friction joint. The resulting response level can be
significantly larger than in the absence of modal interactions. Moreover, it is
shown that the vibration behavior is highly sensitive in the neighborhood of
internal resonances. It is thus concluded that the condition of internal
resonance should be avoided in the design of friction-damped systems.
