Nonlinear model order reduction of jointed structures for dynamic analysis

Assembled structures generally show weak nonlinearity, thus it is rather commonplace to assume that their modes are both linear and uncoupled. At small to modest amplitude, the linearity assumption remains correct in terms of stiffness but, on the contrary, the dissipation in joints is strongly amplitude-dependent. Besides, the modes of any large structure may be LOCALLY collinear in the localized region of a joint. As a result the projection of the structure on normal modes is not appropriate since the corresponding generalized coordinates may be strongly coupled. Instead of using this global basis, the present paper deals with the use of a local basis to reduce the size of the problem without losing the nonlinear physics. Under an appropriate set of assumptions, the method keeps the dynamic properties of joints, even for large amplitude, which include coupling effects, nonlinear damping and softening effects. The formulation enables us to take into account FE models of any realistic geometry. It also gives a straightforward process for experimental identification. The formulation is detailed and investigated on a jointed structure.