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Vehicle occupants are exposed to low frequency vibrations which can adversely affect the ride comfort. Exposure to vibrations can also lead to problems ranging from fatigue and lower back pain to more serious issues like injuries to the spine. The transmission of vibration to seated occupants can be controlled by appropriately designing car seats, which requires a deep understanding of the seat-occupant system behavior. A seat-occupant system is composed of two main components: the seat and the occupant. A key element in the seat, which is a challenge to model, is the flexible polyurethane foam in the seat cushion, which is a nonlinear and viscoelastic material exhibiting behavior on multiple time-scales. The multi-body occupant model is also geometrically nonlinear. The combined model also incorporates profiles of the seat and the occupant, and includes relatively simple friction models at the occupant and seat interfaces.