An efficient reduced order modeling for vibration prediction of geometrically nonlinear structures with friction contact

This paper introduces an original reduced-order model (ROM) for efficient vibration analysis of geometrically nonlinear structures with frictional contact. The proposed approach integrates the IC-Dual method with a free-interface Component Mode Synthesis (Rubin) formulation to capture both global geometric and local contact effects. The reduction basis-comprising linear modes, static fields, and dual modes-is computed on the configuration in which the contact interface is open (i.e., no contact force). It enables the consistent evaluation of nonlinear elastic forces. While all contact configurations can be predicted using this ROM, particular attention is given to cases where loss of contact is possible-where the interplay between geometric and contact nonlinearities is most critical-and transitions to regimes such as slip–stick. Numerical analysis on a cantilever beam with tip friction reveals that even when geometric nonlinearity is weak, neglecting it leads to significant prediction errors due to its influence on contact-state evolution. The proposed ROM accurately captures these effects by incorporating dual modes that enable a precise representation of the influence of axial beam displacement on contact behavior. Moreover, it is shown that contact-induced changes in system stiffness alter the coefficients of the reduced nonlinear elastic stiffness. Both intrusive and nonintrusive implementations achieve accuracy comparable to full-order simulations across all contact configurations while substantially reducing the computational cost.