Engineered structures such as aerospace vehicles experience vibration loads throughout operation necessitating accurate models. Motivated to reduce weight and improve efficiency, modern engineering designs are heavily optimized, increasing the importance of nonlinear effects including friction from bolted joints on the vibration response of these structures. However, new models are needed to fully understand these effects and to efficiently capture nonlinear vibration behavior. First, nonlinear vibration behavior is characterized by amplitude dependent natural frequencies and damping factors. This work improves friction models for bolted joints by incorporating a smooth transition between sticking and slipping, deterministically capturing machining variations, and including permanent deformation of contact points. The resulting model, run on high performance computing (HPC) resources, achieves a good match to experimental results and predicts the low amplitude frequencies of a second assembled structure with less than 3% error. Second, nonlinear vibration behavior results in extra resonance phenomena such as superharmonic resonances. While linear systems respond solely at the forcing frequency, superharmonic resonances are large (locally maximal) responses at an integer multiple of the forcing frequency in nonlinear systems. If unaccounted for, superharmonic resonances can result in structural failures. To efficiently model superharmonic resonances, variable phase resonance nonlinear modes (VPRNM) is developed to track the responses across amplitude levels. Then a reduced order model (ROM) based on VPRNM, termed VPRNM ROM, is proposed to efficiently reconstruct vibration behavior. The VPRNM ROM shows speedups of 4x for construction and 780,000x for evaluation compared to a reference solution. For this work, the reference solutions and VPRNM ROM construction both utilized HPC resources to model a real structure. Furthermore, the VPRNM ROM results are validated against experimental results. Overall, the developed modeling approaches allow for better predictions of nonlinear vibration behavior and efficient understanding of nonlinear vibration effects.
