An "optimal" modal reduction of a system with frictional excitation

The proper orthogonal decomposition theorem is used in an "optimal" modal reduction of a frictionally excited system. The chaotic dynamics are exploited in obtaining a basis that broadly represents the system's dynamics. This basis is used in a Galerkin's approximation to reduce the system order. The reduced model is validated using qualitative and quantitative means and also from the occurrence of bifurcations. The results confirm the validity of the method and expose the benefits of using proper orthogonal modes rather than the linear natural modes of the system. (C) 1999 Academic Press.