Quadratic manifold for model order reduction of a geometrically nonlinear beam with friction contact

This study investigates the application of the quadratic manifold method for model order reduction of geometrically nonlinear structures with friction contact. Quadratic mapping has recently shown its ability to accurately capture the vibrations of a slender structure with geometric nonlinearity. Component Mode Synthesis methods are also well-established reduction approaches for structures with local nonlinearity. These methods allow keeping the contact degrees of freedom (DoFs) in the reduced vector of unknowns and incorporate the corresponding static modes into the reduction basis. In this research, the quadratic manifold method is implemented while contact DoFs are kept in the generalized coordinate vector. So, the manifold is tangent to the subspace spanned by the linear vibration and static modes, and the manifold’s curvature is determined by the static derivatives of the linear vibration modes. The inclusion of the static modes enhances the representation of the behavior of a structure under nonlinear friction forces. The proposed reduction approach is evaluated using a simplified model of a cantilever vibrating beam undergoing rubbing against a wall. The reduced model maintains accuracy while reducing the number of the generalized coordinates compared to a linear manifold, resulting in less online computation time. However, the frequent updating of the projection basis at each iteration imposes an extra online computational burden.