  Modern engineering structures exhibit nonlinear vibration behavior as designs
are pushed to reduce weight and energy consumption. Of specific interest here,
joints in assembled structures introduce friction, hysteresis, and unilateral
contact resulting in nonlinear vibration effects. In many cases, it is
impractical to remove jointed connections necessitating, the understanding of
these behaviors. This work focuses on superharmonic and internal resonances in
hysteretic and jointed systems. Superharmonic resonances occur when a nonlinear
system is forced at an integer fraction of a natural frequency resulting in a
large (locally maximal) response at an integer multiple of the forcing
frequency. When a second vibration mode simultaneously responds in resonance at
the forcing frequency, the combined phenomena is termed an internal resonance.
First, variable phase resonance nonlinear modes (VPRNM) is extended to track
superharmonic resonances in multiple degree of freedom systems exhibiting
hysteresis. Then a novel reduced order model based on VPRNM (VPRNM ROM) is
proposed to reconstruct frequency response curves faster than utilizing the
harmonic balance method (HBM). The VPRNM ROM is demonstrated for a 3 degree of
freedom system with a 3:1 internal resonance and for the jointed Half
Brake-Reuss Beam (HBRB), which exhibits a 7:1 internal resonance. For the HBRB,
new experimental results are used to validate the modeling approaches, and a
previously developed physics-based friction model is further validated,
achieving frequency predictions within 3%. For the considered cases, VPRNM ROM
construction is up to 4 times faster than HBM, and the evaluation of the VPRNM
ROM is up to 780,000 times faster than HBM. The modeling shows that both
tangential slipping and normal direction clapping of the joint play important
roles in exciting the superharmonic resonances in the HBRB.
